Renormalization of Extended QCD2

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Yamamura, Ryo

2015-10-01

Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N_c, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region.

Critical behavior of two- and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems using the effective-field renormalization group technique

NASA Astrophysics Data System (ADS)

Garcia-Adeva, Angel J.; Huber, David L.

2001-07-01

In this work we generalize and subsequently apply the effective-field renormalization-group (EFRG) technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagomé and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced generalized constant coupling method is also applied to the calculation of the critical points and ground-state configurations. Again, a very good agreement is found with exact, Monte Carlo, and renormalization-group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.

Effective field renormalization group approach for Ising lattice spin systems

NASA Astrophysics Data System (ADS)

Fittipaldi, Ivon P.

1994-03-01

A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

Loop Variables in String Theory

NASA Astrophysics Data System (ADS)

Sathiapalan, B.

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space-time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

Self-diffusion in a system of interacting Langevin particles

NASA Astrophysics Data System (ADS)

Dean, D. S.; Lefèvre, A.

2004-06-01

The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature β and the particle density ρ . The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small β and ρβ constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.

Functional renormalization group approach to SU(N ) Heisenberg models: Real-space renormalization group at arbitrary N

NASA Astrophysics Data System (ADS)

Buessen, Finn Lasse; Roscher, Dietrich; Diehl, Sebastian; Trebst, Simon

2018-02-01

The pseudofermion functional renormalization group (pf-FRG) is one of the few numerical approaches that has been demonstrated to quantitatively determine the ordering tendencies of frustrated quantum magnets in two and three spatial dimensions. The approach, however, relies on a number of presumptions and approximations, in particular the choice of pseudofermion decomposition and the truncation of an infinite number of flow equations to a finite set. Here we generalize the pf-FRG approach to SU (N )-spin systems with arbitrary N and demonstrate that the scheme becomes exact in the large-N limit. Numerically solving the generalized real-space renormalization group equations for arbitrary N , we can make a stringent connection between the physically most significant case of SU(2) spins and more accessible SU (N ) models. In a case study of the square-lattice SU (N ) Heisenberg antiferromagnet, we explicitly demonstrate that the generalized pf-FRG approach is capable of identifying the instability indicating the transition into a staggered flux spin liquid ground state in these models for large, but finite, values of N . In a companion paper [Roscher et al., Phys. Rev. B 97, 064416 (2018), 10.1103/PhysRevB.97.064416] we formulate a momentum-space pf-FRG approach for SU (N ) spin models that allows us to explicitly study the large-N limit and access the low-temperature spin liquid phase.

On the effective field theory of intersecting D3-branes

NASA Astrophysics Data System (ADS)

Abbaspur, Reza

2018-05-01

We study the effective field theory of two intersecting D3-branes with one common dimension along the lines recently proposed in ref. [1]. We introduce a systematic way of deriving the classical effective action to arbitrary orders in perturbation theory. Using a proper renormalization prescription to handle logarithmic divergencies arising at all orders in the perturbation series, we recover the first order renormalization group equation of ref. [1] plus an infinite set of higher order equations. We show the consistency of the higher order equations with the first order one and hence interpret the first order result as an exact RG flow equation in the classical theory.

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

NASA Astrophysics Data System (ADS)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory.

PubMed

Yunus, Çağın; Renklioğlu, Başak; Keskin, Mustafa; Berker, A Nihat

2016-06-01

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

Renormalization group invariant of lepton Yukawa couplings

NASA Astrophysics Data System (ADS)

Tsuyuki, Takanao

2015-04-01

By using quark Yukawa matrices only, we can construct renormalization invariants that are exact at the one-loop level in the standard model. One of them, Iq, is accidentally consistent with unity, even though quark masses are strongly hierarchical. We calculate a lepton version of the invariant Il for Dirac and Majorana neutrino cases and find that Il can also be close to unity. For the Dirac neutrino and inverted hierarchy case, if the lightest neutrino mass is 3.0 meV to 8.8 meV, an equality Iq=Il can be satisfied. These invariants are not changed even if new particles couple to the standard model particles, as long as those couplings are generation independent.

τ hadronic spectral function moments in a nonpower QCD perturbation theory

NASA Astrophysics Data System (ADS)

Abbas, Gauhar; Ananthanarayan, B.; Caprini, I.; Fischer, J.

2016-04-01

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling and other QCD parameters from the hadronic decays of the τ lepton. We consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ;reference model;, including moments that are poorly described by the standard expansions.

Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering

NASA Astrophysics Data System (ADS)

Atalay, Bora; Berker, A. Nihat

2018-05-01

Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states q =3 ,4 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d >1 and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling q ×q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1 +ɛ , the system is as expected disordered at all temperatures for d =1 .

Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

PubMed

Saveliev, V L; Gorokhovski, M A

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

NASA Astrophysics Data System (ADS)

Saveliev, V. L.; Gorokhovski, M. A.

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

A Study in HRT Resolution: Seeking Maximum Sensitivity Among Variations in Sensing Element Material

NASA Technical Reports Server (NTRS)

Morales, Jeremy M.

2005-01-01

The EXACT (Experiments Along Coexistence near Tricriticality) project endeavors to perform the most rigorous test to date of Renormalization Group theory. In most cases, the theory gives only approximate solutions, but it offers exact predictions in the case of the He-3-He-4 tricritical point. Currently, the project is focused on maximizing the performance of the low-temperature system's HRT (high resolution thermometer) near the tricritical point. The HRT uses a PdMn sensing element, the qualities of which change based on its Mn concentration and whether or not it is annealed. All sensing element combinations will be catalogued, and through the data, the optimum configuration will be reported.

The Poisson-Boltzmann theory for the two-plates problem: some exact results.

PubMed

Xing, Xiang-Jun

2011-12-01

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

Local renormalization group functions from quantum renormalization group and holographic bulk locality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Yu

Here, the bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographicmore » renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.« less

Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective

NASA Technical Reports Server (NTRS)

Zhou, Ye; McComb, W. David; Vahala, George

1997-01-01

The term renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization group to turbulence modelling.

Infinitely robust order and local order-parameter tulips in Apollonian networks with quenched disorder

NASA Astrophysics Data System (ADS)

Kaplan, C. Nadir; Hinczewski, Michael; Berker, A. Nihat

2009-06-01

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.

Spectral Function and Quasiparticle Damping of Interacting Bosons in Two Dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinner, Andreas; Kopietz, Peter; Hasselmann, Nils

2009-03-27

We employ the functional renormalization group to study dynamical properties of the two-dimensional Bose gas. Our approach is free of infrared divergences, which plague the usual diagrammatic approaches, and is consistent with the exact Nepomnyashchy identity, which states that the anomalous self-energy vanishes at zero frequency and momentum. We recover the correct infrared behavior of the propagators and present explicit results for the spectral line shape, from which we extract the quasiparticle dispersion and dampi0008.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

RG flows for λ-deformed CFTs

NASA Astrophysics Data System (ADS)

Sagkrioti, E.; Sfetsos, K.; Siampos, K.

2018-05-01

We study the renormalization group equations of the fully anisotropic λ-deformed CFTs involving the direct product of two current algebras at different levels k1,2 for general semi-simple groups. The exact, in the deformation parameters, β-function is found via the effective action of the quantum fluctuations around a classical background as well as from gravitational techniques. Furthermore, agreement with known results for symmetric couplings and/or for equal levels, is demonstrated. We study in detail the two coupling case arising by splitting the group into a subgroup and the corresponding coset manifold which consistency requires to be either a symmetric-space one or a non-symmetric Einstein-space.

Excited state TBA and renormalized TCSA in the scaling Potts model

NASA Astrophysics Data System (ADS)

Lencsés, M.; Takács, G.

2014-09-01

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.

Surprises in low-dimensional correlated systems

NASA Astrophysics Data System (ADS)

Lin, Hsiu-Hau

In this thesis, correlation effects in low-dimensional systems were studied. In particular, we focus on two systems: a point-contact in the quantum-Hall regime under the influence of ac drive and quasi-one-dimensional ladder materials with generic interactions in weak coupling. Powerful techniques, including renormalization group, quantum field theory, operator product expansions, bosonization,...etc., were employed to extract surprising physics out of these strongly fluctuating systems. We first study the effect of an ac drive on the current-voltage (I-V) characteristics of a tunnel junction between two fractional Quantum Hall fluids at filling nu-1 an odd integer. In a semi-classical limit, the tunneling current exhibits mode-locking, which corresponds to plateaus in the I-V curve at integer multiples of I = ef , with f the ac drive frequency. However, the full quantum model exhibits rounded plateaus centered around the quantized current values due to quantum fluctuations. The locations of these plateaus can serve as an indirect hint of fractional charges. Switching attentions to quasi-one-dimensional coupled-chain systems, we present a systematic weak-coupling renormalization group (RG) technique and find that generally broad regions of the phase space of the ladder materials are unstable to pairing, usually with approximate d-wave symmetry. The dimensional crossovers from 1D to 2D were also discussed. Carbon nanotubes as possible candidates that display such unconventional pairing and interesting physics in weak coupling were discussed. Quite surprisingly, a hidden symmetry was found in the weakly-coupled two-leg ladder. A perturbative renormalization group analysis reveals that at half-filling the model scales onto an exactly soluble SO(8) symmetric Gross-Neveu model. Integrability of the Gross-Neveu model is employed to extract the exact energies, degeneracies and quantum numbers of all the low energy excited states, which fall into degenerate SO(8) multiplets. For generic physical interactions, there are four robust phases which have different SO(8) symmetries but share a common SO(5) symmetry. The effects of marginal chiral interactions were discussed at the end. Finally, we summarize our main results and discuss related open questions for future study.

Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions.

PubMed

Wang, Wenlong; Moore, M A; Katzgraber, Helmut G

2018-03-01

The fractal dimension of domain walls produced by changing the boundary conditions from periodic to antiperiodic in one spatial direction is studied using both the strong-disorder renormalization group algorithm and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or fewer space dimensions, the fractal dimension is lower than the space dimension. This means that interfaces are not space filling, thus implying that replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space dimension in six dimensions, indicating that replica symmetry breaking occurs above six dimensions. In two space dimensions, the strong-disorder renormalization group results for the fractal dimension are in good agreement with essentially exact numerical results, but the small difference is significant. We discuss the origin of this close agreement. For the greedy algorithm there is analytical expectation that the fractal dimension is equal to the space dimension in six dimensions and our numerical results are consistent with this expectation.

NLO renormalization in the Hamiltonian truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hill, Christopher T.

We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEV's of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.

Duality in a supersymmetric gauge theory from a perturbative viewpoint

NASA Astrophysics Data System (ADS)

Ryttov, Thomas A.; Shrock, Robert

2018-03-01

We study duality in N =1 supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities a , c , a /c , and b at superconformal fixed points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities and suggest possible implications for nonsupersymmetric theories.

Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions

DOE PAGES

Jia, Shaoyang; Pennington, Michael R.

2017-04-10

Here, we explore the dependence of fermion propagators on the covariant gauge fixing parameter in quantum electrodynamics (QED) with the number of spacetime dimensions kept explicit. Gauge covariance is controlled by the the Landau -Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature, the LKFT for a fermion propagator in Minkowski space is solved exactly. The special scenario of 3D has been used to test claims made for general cases. When renormalized correctly, the simplification of the LKFT in 4D has been achieved with the help of fractional calculus.

Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chin, Alex W.; Rivas, Angel; Huelga, Susana F.

2010-09-15

By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain systemmore » for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.« less

Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling

NASA Astrophysics Data System (ADS)

Wu, Xing-Gang; Shen, Jian-Ming; Du, Bo-Lun; Brodsky, Stanley J.

2018-05-01

As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. In this paper, we show that by using the newly suggested C -scheme coupling, one can obtain a demonstration that the principle of maximum conformality prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the nonsinglet Adler function and for τ decay to ν + hadrons at the four-loop level.

Universality, twisted fans, and the Ising model. [Renormalization, two-loop calculations, scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dash, J.W.; Harrington, S.J.

1975-06-24

Critical exponents are evaluated for the Ising model using universality in the form of ''twisted fans'' previously introduced in Reggeon field theory. The universality is with respect to scales induced through renormalization. Exact twists are obtained at ..beta.. = 0 in one loop for D = 2,3 with ..nu.. = 0.75 and 0.60 respectively. In two loops one obtains ..nu.. approximately 1.32 and 0.68. No twists are obtained for eta, however. The results for the standard two loop calculations are also presented as functions of a scale.

Aspects of Higher-Spin Conformal Field Theories and Their Renormalization Group Flows

NASA Astrophysics Data System (ADS)

Diab, Kenan S.

In this thesis, we study conformal field theories (CFTs) with higher-spin symmetry and the renormalization group flows of some models with interactions that weakly break the higher-spin symmetry. When the higher-spin symmetry is exact, we will present CFT analogues of two classic results in quantum field theory: the Coleman-Mandula theorem, which is the subject of chapter 2, and the Weinberg-Witten theorem, which is the subject of chapter 3. Schematically, our Coleman-Mandula analogue states that a CFT that contains a symmetric conserved current of spin s > 2 in any dimension d > 3 is effectively free, and our Weinberg-Witten analogue states that the presence of certain short, higher-spin, "sufficiently asymmetric" representations of the conformal group is either inconsistent with conformal symmetry or leads to free theories in d = 4 dimensions. In both chapters, the basic strategy is to solve certain Ward identities in convenient kinematical limits and thereby show that the number of solutions is very limited. In the latter chapter, Hofman-Maldacena bounds, which constrain one-point functions of the stress tensor in general states, play a key role. Then, in chapter 4, we will focus on the particular examples of the O(N) and Gross-Neveu model in continuous dimensions. Using diagrammatic techniques, we explicitly calculate how the coefficients of the two-point function of a U(1) current and the two-point function of the stress tensor (CJ and CT, respectively) are renormalized in the 1/N and epsilon expansions. From the higher-spin perspective, these models are interesting since they are related via the AdS/CFT correspondence to Vasiliev gravity. In addition to checking and extending a number of previously-known results about CT and CJ in these theories, we find that in certain dimensions, CJ and CT are not monotonic along the renormalization group flow. Although it was already known that certain supersymmetric models do not satisfy a "CJ"- or " CT"-theorem, this shows that such a theorem is unlikely to hold even under more restrictive assumptions.

Higher derivative couplings in theories with sixteen supersymmetries

DOE PAGES

Lin, Ying -Hsuan; Shao, Shu -Heng; Yin, Xi; ...

2015-12-15

We give simple arguments for new non-renormalization theorems on higher derivative couplings of gauge theories to supergravity, with sixteen supersymmetries, by considerations of brane-bulk superamplitudes. This leads to some exact results on the effective coupling of D3-branes in type IIB string theory. As a result, we also derive exact results on higher dimensional operators in the torus compactification of the six dimensional (0, 2) superconformal theory.

Sign Reversal of Coulom Interaction Between Two Quasiparticles in Momentum Space

NASA Astrophysics Data System (ADS)

Fan, J. D.; Malozovsky, Yuriy M.

2013-06-01

The main misconception regarding the interaction between quasiparticles stems from the assertion that the interaction energy between two quasiparticles is exactly identical to that of the renormalized interaction between two particles due to interparticle interaction in the Fermi system. If the main concept regarding the definition of quasiparticle as a weakly excited state of the Fermi system with conservation of charge and spin is paramount (except for the charge and spin separation models), the concept of the interaction between quasiparticles is very different from the assumption in the common sense. In this paper, we will prove a general theorem that the interaction between two quasiparticles is very much different from the renormalized interaction between two particles. The major difference lies in two places: the interaction between two quasiparticles is just negative to the renormalized interaction between two particles, and the interaction energy between the two particles is proportional to the product of two Fermi liquid renormalization factors. The result shed light on the reinterpretation of Cooper's pairing without invoking electron-photon interaction.

Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

NASA Astrophysics Data System (ADS)

Nataf, Pierre; Mila, Frédéric

2018-04-01

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Comprehensive renormalization group analysis of the littlest seesaw model

NASA Astrophysics Data System (ADS)

Geib, Tanja; King, Stephen F.

2018-04-01

We present a comprehensive renormalization group analysis of the littlest seesaw model involving two right-handed neutrinos and a very constrained Dirac neutrino Yukawa coupling matrix. We perform the first χ2 analysis of the low energy masses and mixing angles, in the presence of renormalization group corrections, for various right-handed neutrino masses and mass orderings, both with and without supersymmetry. We find that the atmospheric angle, which is predicted to be near maximal in the absence of renormalization group corrections, may receive significant corrections for some nonsupersymmetric cases, bringing it into close agreement with the current best fit value in the first octant. By contrast, in the presence of supersymmetry, the renormalization group corrections are relatively small, and the prediction of a near maximal atmospheric mixing angle is maintained, for the studied cases. Forthcoming results from T2K and NO ν A will decisively test these models at a precision comparable to the renormalization group corrections we have calculated.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

Tensor renormalization group methods for spin and gauge models

NASA Astrophysics Data System (ADS)

Zou, Haiyuan

The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

The generalized scheme-independent Crewther relation in QCD

NASA Astrophysics Data System (ADS)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; Brodsky, Stanley J.

2017-07-01

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton-nucleon scattering times the Adler function, defined from the cross section for electron-positron annihilation into hadrons, has no pQCD radiative corrections. The ;Generalized Crewther Relation; relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp) at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp-1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd (Q) =∑i≥1 αˆg1 i (Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.

Collision group and renormalization of the Boltzmann collision integral.

PubMed

Saveliev, V L; Nanbu, K

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Collision group and renormalization of the Boltzmann collision integral

NASA Astrophysics Data System (ADS)

Saveliev, V. L.; Nanbu, K.

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System

NASA Astrophysics Data System (ADS)

Kim, Chungku

2018-06-01

We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.

Renormalization scheme dependence of high-order perturbative QCD predictions

NASA Astrophysics Data System (ADS)

Ma, Yang; Wu, Xing-Gang

2018-02-01

Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the sensitivity of pQCD prediction on the scheme parameters by using the scheme-dependent {βm ≥2}-terms. We adopt two four-loop examples, e+e-→hadrons and τ decays into hadrons, for detailed analysis. Our results show that under the conventional scale setting, by including more-and-more loop terms, the scheme dependence of the pQCD prediction cannot be reduced as efficiently as that of the scale dependence. Thus a proper scale-setting approach should be important to reduce the scheme dependence. We observe that the principle of minimum sensitivity could be such a scale-setting approach, which provides a practical way to achieve optimal scheme and scale by requiring the pQCD approximate be independent to the "unphysical" theoretical conventions.

One-loop renormalization of Lee-Wick gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grinstein, Benjamin; O'Connell, Donal

2008-11-15

We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theorymore » than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.« less

Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

NASA Astrophysics Data System (ADS)

Nadir Kaplan, C.; Hinczewski, Michael; Berker, A. Nihat

2009-03-01

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder.[1] We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns. [1] C.N. Kaplan, M. Hinczewski, and A.N. Berker, arXiv:0811.3437v1 [cond-mat.dis-nn] (2008).

Quantum critical spin-2 chain with emergent SU(3) symmetry.

PubMed

Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

2015-04-10

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Experimental observation of the 1/3 magnetization plateau in the diamond-chain compound Cu3(CO3)2(OH)2.

PubMed

Kikuchi, H; Fujii, Y; Chiba, M; Mitsudo, S; Idehara, T; Tonegawa, T; Okamoto, K; Sakai, T; Kuwai, T; Ohta, H

2005-06-10

The magnetic susceptibility, high field magnetization, and specific heat measurements of Cu3(CO3)2(OH)2, which is a model substance for the frustrating diamond spin chain model, have been performed using single crystals. Two broad peaks are observed at around 20 and 5 K in both magnetic susceptibility and specific heat results. The magnetization curve has a clear plateau at one third of the saturation magnetization. The experimental results are examined in terms of theoretical expectations based on exact diagonalization and density matrix renormalization group methods. An origin of magnetic anisotropy is also discussed.

Interband excitations in the 1D limit of two-band fractional Chern insulators

NASA Astrophysics Data System (ADS)

Jaworowski, Błażej; Kaczmarkiewicz, Piotr; Potasz, Paweł; Wójs, Arkadiusz

2018-05-01

We investigate the stability of the one-dimensional limit of ν = 1 / 3 Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system - the checkerboard lattice.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

DOE PAGES

Jia, Shaoyang; Pennington, M. R.

2017-08-01

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Shaoyang; Pennington, M. R.

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Renormalization group approach to power-law modeling of complex metabolic networks.

PubMed

Hernández-Bermejo, Benito

2010-08-07

In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations. Copyright 2010 Elsevier Ltd. All rights reserved.

Fermionic influence on inflationary fluctuations

NASA Astrophysics Data System (ADS)

Boyanovsky, Daniel

2016-04-01

Motivated by apparent persistent large scale anomalies in the cosmic microwave background we study the influence of fermionic degrees of freedom on the dynamics of inflaton fluctuations as a possible source of violations of (nearly) scale invariance on cosmological scales. We obtain the nonequilibrium effective action of an inflaton-like scalar field with Yukawa interactions (YD ,M) to light fermionic degrees of freedom both for Dirac and Majorana fields in de Sitter space-time. The effective action leads to Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and a stochastic Gaussian noise. We solve the Langevin equation in the super-Hubble limit implementing a dynamical renormalization group resummation. For a nearly massless inflaton its power spectrum of super-Hubble fluctuations is enhanced, P (k ;η )=(H/2 π )2eγt[-k η ] with γt[-k η ]=1/6 π2 [∑i =1 NDYi,D 2+2 ∑j =1 NMYj,M 2]{ln2[-k η ]-2 ln [-k η ]ln [-k η0]} for ND Dirac and NM Majorana fermions, and η0 is the renormalization scale at which the inflaton mass vanishes. The full power spectrum is shown to be renormalization group invariant. These corrections to the super-Hubble power spectrum entail a violation of scale invariance as a consequence of the coupling to the fermionic fields. The effective action is argued to be exact in the limit of a large number of fermionic fields. A cancellation between the enhancement from fermionic degrees of freedom and suppression from light scalar degrees of freedom conformally coupled to gravity suggests the possibility of a finely tuned supersymmetry among these fields.

The International Conference on Amorphous and Liquid Semiconductors (9th).

DTIC Science & Technology

1979-12-11

loop effective action of a constant gluon field can be expressed in terms of the experimentally determinable A,.,• In the following chapter, the...regularization and Schwinger’s proper time method. The renormalization mass parameters appearing in the two treatments can then be related and the exact one

Functional Renormalization Group Flows on Friedman-Lemaître-Robertson-Walker backgrounds

NASA Astrophysics Data System (ADS)

Platania, Alessia; Saueressig, Frank

2018-06-01

We revisit the construction of the gravitational functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein-Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the causal dynamical triangulations approach to quantum gravity.

The ab-initio density matrix renormalization group in practice.

PubMed

Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodrigues, Davi C.; Piattella, Oliver F.; Chauvineau, Bertrand, E-mail: davi.rodrigues@cosmo-ufes.org, E-mail: Bertrand.Chauvineau@oca.eu, E-mail: oliver.piattella@pq.cnpq.br

We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids.

Threshold and flavor effects in the renormalization group equations of the MSSM: Dimensionless couplings

NASA Astrophysics Data System (ADS)

Box, Andrew D.; Tata, Xerxes

2008-03-01

In a theory with broken supersymmetry, gaugino couplings renormalize differently from gauge couplings, as do higgsino couplings from Higgs boson couplings. As a result, we expect the gauge (Higgs boson) couplings and the corresponding gaugino (higgsino) couplings to evolve to different values under renormalization group evolution. We reexamine the renormalization group equations (RGEs) for these couplings in the minimal supersymmetric standard model (MSSM). To include threshold effects, we calculate the β functions using a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We find that the difference between the SM couplings and their SUSY cousins that is ignored in the literature may be larger than two-loop effects which are included, and further that renormalization group evolution induces a nontrivial flavor structure in gaugino interactions. We present here the coupled set of RGEs for these dimensionless gauge and Yukawa-type couplings. The RGEs for the dimensionful soft-supersymmetry-breaking parameters of the MSSM will be presented in a companion paper.

The generalized scheme-independent Crewther relation in QCD

DOE PAGES

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; ...

2017-05-10

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

The generalized scheme-independent Crewther relation in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

PubMed

Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2012-07-01

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

Renormalization-group theory of plasma microturbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carati, D.; Chriaa, K.; Balescu, R.

1994-08-01

The dynamical renormalization-group methods are applied to the gyrokinetic equation describing drift-wave turbulence in plasmas. As in both magnetohydrodynamic and neutral turbulence, small-scale fluctuations appear to act as effective dissipative processes on large-scale phenomena. A linear renormalized gyrokinetic equation is derived. No artificial forcing is introduced into the equations and all the renormalized corrections are expressed in terms of the fluctuating electric potential. The link with the quasilinear limit and the direct interaction approximation is investigated. Simple analytical expressions for the anomalous transport coefficients are derived by using the linear renormalized gyrokinetic equation. Examples show that both quasilinear and Bohmmore » scalings can be recovered depending on the spectral amplitude of the electric potential fluctuations.« less

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

NASA Astrophysics Data System (ADS)

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

2016-07-01

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

PubMed

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R

2016-07-07

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Renormalization-group theory for the eddy viscosity in subgrid modeling

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George; Hossain, Murshed

1988-01-01

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Renormalization group independence of Cosmological Attractors

NASA Astrophysics Data System (ADS)

Fumagalli, Jacopo

2017-06-01

The large class of inflationary models known as α- and ξ-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters (ns , r) are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation (which is a particular ξ-attractor) this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.

Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Démery, Vincent; Rosso, Alberto

2018-06-01

The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force . At small disorder, we unveil an intermediary linear regime for characterized by the renormalized mobility . Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

Space and time renormalization in phase transition dynamics

DOE PAGES

Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; ...

2016-02-18

Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigatingmore » an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.« less

Random-walk approach to the d -dimensional disordered Lorentz gas

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

Effective-field renormalization-group method for Ising systems

NASA Astrophysics Data System (ADS)

Fittipaldi, I. P.; De Albuquerque, D. F.

1992-02-01

A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

2009-10-01

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

Renormalization of concurrence: The application of the quantum renormalization group to quantum-information systems

NASA Astrophysics Data System (ADS)

Kargarian, M.; Jafari, R.; Langari, A.

2007-12-01

We have combined the idea of renormalization group and quantum-information theory. We have shown how the entanglement or concurrence evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. Moreover, we introduce how the renormalization-group approach can be implemented to obtain the quantum-information properties of a many-body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one-dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length.

Renormalization-group constraints on Yukawa alignment in multi-Higgs-doublet models

NASA Astrophysics Data System (ADS)

Ferreira, P. M.; Lavoura, L.; Silva, João P.

2010-05-01

We write down the renormalization-group equations for the Yukawa-coupling matrices in a general multi-Higgs-doublet model. We then assume that the matrices of the Yukawa couplings of the various Higgs doublets to right-handed fermions of fixed quantum numbers are all proportional to each other. We demonstrate that, in the case of the two-Higgs-doublet model, this proportionality is preserved by the renormalization-group running only in the cases of the standard type-I, II, X, and Y models. We furthermore show that a similar result holds even when there are more than two Higgs doublets: the Yukawa-coupling matrices to fermions of a given electric charge remain proportional under the renormalization-group running if and only if there is a basis for the Higgs doublets in which all the fermions of a given electric charge couple to only one Higgs doublet.

Fractional charge and emergent mass hierarchy in diagonal two-leg t – J cylinders

DOE PAGES

Jiang, Yi-Fan; Jiang, Hong-Chen; Yao, Hong; ...

2017-06-06

Here, we define a class of “diagonal” tmore » $-$ J ladders rotated by π / 4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group. Here, we focus on the two-leg cylinder with a doped hole concentration near x = $$\\frac{1}{4}$$ . At exactly x = $$\\frac{1}{4}$$, the system forms a period 4 charge density wave and exhibits spin-charge separation. Slightly away from $$\\frac{1}{4}$$ doping, we observe several topologically distinct types of solitons with well-defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.« less

Large N critical exponents for the chiral Heisenberg Gross-Neveu universality class

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2018-05-01

We compute the large N critical exponents η , ηϕ and 1 /ν in d dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of 1 /N . For instance, the large N conformal bootstrap method is used to determine η at O (1 /N3) while the other exponents are computed to O (1 /N2). Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behavior of the exponents in 2

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Functional renormalization group analysis of tensorial group field theories on Rd

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele

2016-07-01

Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

NASA Astrophysics Data System (ADS)

Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai Johannes; Rejzner, Katarzyna

2014-12-01

We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

Improved Monte Carlo Renormalization Group Method

DOE R&D Accomplishments Database

Gupta, R.; Wilson, K. G.; Umrigar, C.

1985-01-01

An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.

Signal inference with unknown response: calibration-uncertainty renormalized estimator.

PubMed

Dorn, Sebastian; Enßlin, Torsten A; Greiner, Maksim; Selig, Marco; Boehm, Vanessa

2015-01-01

The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.

Multiscale unfolding of real networks by geometric renormalization

NASA Astrophysics Data System (ADS)

García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

2018-06-01

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

Renormalization group estimates of transport coefficients in the advection of a passive scalar by incompressible turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George

1993-01-01

The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that higher order nonlinearities do not contribute as k goes to 0, but have an essential role as k goes to k(sub c) the cutoff wave number separating the resolvable scales from the sub grid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.

Renormalization group, normal form theory and the Ising model

NASA Astrophysics Data System (ADS)

Raju, Archishman; Hayden, Lorien; Clement, Colin; Liarte, Danilo; Sethna, James

The results of the renormalization group are commonly advertised as the existence of power law singularities at critical points. Logarithmic and exponential corrections are seen as special cases and dealt with on a case-by-case basis. We propose to systematize computing the singularities in the renormalization group using perturbative normal form theory. This gives us a way to classify all such singularities in a unified framework and to generate a systematic machinery to do scaling collapses. We show that this procedure leads to some new results even in classic cases like the Ising model and has general applicability.

Hypercuboidal renormalization in spin foam quantum gravity

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Steinhaus, Sebastian

2017-06-01

In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

The { β}-expansion formalism in perturbative QCD and its extension

NASA Astrophysics Data System (ADS)

Kataev, A. L.; Mikhailov, S. V.

2016-11-01

We discuss the { β}-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ R-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the { β}-expansion. We illustrate this feature considering the nonsinglet Adler function D NS in the third order of perturbation. We propose a generalization of the { β}-expansion for the renormalization group covariant quantities — the { β, γ}-expansion.

Spin-triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li0.9Mo6O17

NASA Astrophysics Data System (ADS)

Cho, Weejee; Platt, Christian; McKenzie, Ross H.; Raghu, Srinivas

2015-10-01

The purple bronze Li0.9Mo6O17 is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin-triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has more sign changes than required by the point-group symmetry.

Spin triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li0.9 Mo6 O17

NASA Astrophysics Data System (ADS)

Platt, Christian; Cho, Weejee; McKenzie, Ross H.; Raghu, Sri

The purple bronze Li0.9Mo6O17 is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four Molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has accidental nodes, i.e. it has more sign changes than required by the point-group symmetry.

String Theory: exact solutions, marginal deformations and hyperbolic spaces

NASA Astrophysics Data System (ADS)

Orlando, Domenico

2006-10-01

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces.

Holography for Schrödinger backgrounds

NASA Astrophysics Data System (ADS)

Guica, Monica; Skenderis, Kostas; Taylor, Marika; van Rees, Balt C.

2011-02-01

We discuss holography for Schrödinger solutions of both topologically massive gravity in three dimensions and massive vector theories in ( d + 1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrödinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k v . We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction.

TOPICAL REVIEW: Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

NASA Astrophysics Data System (ADS)

Meurice, Y.

2007-06-01

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigourous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and functional RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review is to present a configuration space counterpart, suitable for lattice formulations, of functional RG equations formulated in momentum space (often called exact RG equations and abbreviated ERGE).

Variational Approach to Monte Carlo Renormalization Group

NASA Astrophysics Data System (ADS)

Wu, Yantao; Car, Roberto

2017-12-01

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

Exact results for the O( N ) model with quenched disorder

NASA Astrophysics Data System (ADS)

Delfino, Gesualdo; Lamsen, Noel

2018-04-01

We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O( N )-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as N varies, between the first two classes. For positive N , it contains a single line of infrared fixed points spanning the values of N from √{2}-1 to 1. The symmetry sector of the energy density operator is superuniversal (i.e. N -independent) along this line. For N = 2 a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.

Site-occupation embedding theory using Bethe ansatz local density approximations

NASA Astrophysics Data System (ADS)

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

2018-06-01

Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

2015-03-01

We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

Entanglement renormalization and topological order.

PubMed

Aguado, Miguel; Vidal, Guifré

2008-02-22

The multiscale entanglement renormalization ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network. Kitaev states on an infinite lattice are also shown to be a fixed point of the renormalization group flow associated with entanglement renormalization. All of these results generalize to arbitrary quantum double models.

Functional renormalization group for the U (1 )-T56 tensorial group field theory with closure constraint

NASA Astrophysics Data System (ADS)

Lahoche, Vincent; Ousmane Samary, Dine

2017-02-01

This paper is focused on the functional renormalization group applied to the T56 tensor model on the Abelian group U (1 ) with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.

The renormalization group method in statistical hydrodynamics

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.

1994-09-01

This paper gives a first principles formulation of a renormalization group (RG) method appropriate to study of turbulence in incompressible fluids governed by Navier-Stokes equations. The present method is a momentum-shell RG of Kadanoff-Wilson type based upon the Martin-Siggia-Rose (MSR) field-theory formulation of stochastic dynamics. A simple set of diagrammatic rules are developed which are exact within perturbation theory (unlike the well-known Ma-Mazenko prescriptions). It is also shown that the claim of Yakhot and Orszag (1986) is false that higher-order terms are irrelevant in the ɛ expansion RG for randomly forced Navier-Stokes (RFNS) with power-law force spectrum F̂(k)=D0k-d+(4-ɛ). In fact, as a consequence of Galilei covariance, there are an infinite number of higher-order nonlinear terms marginal by power counting in the RG analysis of the power-law RFNS, even when ɛ≪4. The difficulty does not occur in the Forster-Nelson-Stephen (FNS) RG analysis of thermal fluctuations in an equilibrium NS fluid, which justifies a linear regression law for d≳2. On the other hand, the problem occurs also at the nontrivial fixed point in the FNS Model A, or its Burgers analog, when d<2. The marginal terms can still be present at the strong-coupling fixed point in true NS turbulence. If so, infinitely many fixed points may exist in turbulence and be associated to a somewhat surprising phenomenon: nonuniversality of the inertial-range scaling laws depending upon the dissipation-range dynamics.

Ab initio excited states from the in-medium similarity renormalization group

NASA Astrophysics Data System (ADS)

Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.

2017-04-01

We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

DOE PAGES

Bi, Huan -Yu; Wu, Xing -Gang; Ma, Yang; ...

2015-06-26

The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R δ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfymore » all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio R e+e– and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {β i}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.« less

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Sodemann, Inti; Sheng, D. N.; Fu, Liang

2017-05-01

We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n =1 ) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

PyR@TE. Renormalization group equations for general gauge theories

NASA Astrophysics Data System (ADS)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

Density matrix renormalization group with efficient dynamical electron correlation through range separation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

2015-06-14

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

Pointless strings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Periwal, V.

1988-01-01

The author proves that bosonic string perturbation theory diverges and is not Borel summable. This is an indication of a non-perturbative instability of the bosonic string vacuum. He formulates two-dimensional sigma models in terms of algebras of functions. He extends this formulation to general C* algebras. He illustrates the utility of these algebraic notions by calculating some determinants of interest in the study of string propagation in orbifold backgrounds. He studies the geometry of spaces of field theories and show that the vanishing of the curvature of the natural Gel'fand-Naimark-Segal metric on such spaces is exactly the strong associativity conditionmore » of the operator product expansion.He shows that string scattering amplitudes arise as invariants of renormalization, when he formulates renormalization in terms of rescalings of the metric on the string world-sheet.« less

High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-10-01

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d = 2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d ≥ 3.

Capturing nonlocal interaction effects in the Hubbard model: Optimal mappings and limits of applicability

NASA Astrophysics Data System (ADS)

van Loon, E. G. C. P.; Schüler, M.; Katsnelson, M. I.; Wehling, T. O.

2016-10-01

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant quantum Monte Carlo simulations of the effective Hubbard model.

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Gyro-viscosity and linear dispersion relations in pair-ion magnetized plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kono, M.; Vranjes, J.; Departamento de Astrofisica, Universidad de La Laguna, Tenerife E38205

2015-11-15

A fluid theory has been developed by taking account of gyro-viscosity to study wave propagation characteristics in a homogeneous pair-ion magnetized plasma with a cylindrical symmetry. The exact dispersion relations derived by the Hankel-Fourier transformation are shown comparable with those observed in the experiment by Oohara and co-workers. The gyro-viscosity is responsible for the change in propagation characteristics of the ion cyclotron wave from forward to backward by suppressing the effect of the thermal pressure which normally causes the forward nature of dispersion. Although the experiment has been already explained by a kinetic theory by the present authors, the kineticmore » derivations are so involved because of exact particle orbits in phase space, finite Lamor radius effects, and higher order ion cyclotron resonances. The present fluid theory provides a simple and transparent structure to the dispersion relations since the gyro-viscosity is renormalized into the ion cyclotron frequency which itself indicates the backward nature of dispersion. The usual disadvantage of a fluid theory, which treats only fundamental modes of eigen-waves excited in a system and is not able to describe higher harmonics that a kinetic theory does, is compensated by simple derivations and clear picture based on the renormalization of the gyro-viscosity.« less

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

NASA Astrophysics Data System (ADS)

Rose, F.; Dupuis, N.

2018-05-01

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

Renormalization group fixed points of foliated gravity-matter systems

NASA Astrophysics Data System (ADS)

Biemans, Jorn; Platania, Alessia; Saueressig, Frank

2017-05-01

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

Turbulent transport of a passive-scalar field by using a renormalization-group method

NASA Technical Reports Server (NTRS)

Hossain, Murshed

1992-01-01

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

PubMed

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

Renormalization group flow of the Higgs potential

NASA Astrophysics Data System (ADS)

Gies, Holger; Sondenheimer, René

2018-01-01

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue `Higgs cosmology'.

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

NASA Astrophysics Data System (ADS)

Merker, L.; Costi, T. A.

2012-08-01

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.

Effect of Interaction on the Majorana Zero Modes in the Kitaev Chain at Half Filling

NASA Astrophysics Data System (ADS)

Li, Zhidan; Han, Qiang

2018-04-01

The one dimension interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations and various physical quantities as functions of the fermion-fermion interaction $U$ are calculated systematically using the density matrix renormalization group method. A special value of interaction $U_p$ is revealed in the topological region of the phase diagram. We show that at $U_p$ the ground states are strictly two-fold degenerate even though the chain length is finite and the zero-energy peak due to the Majorana zero modes is maximally enhanced and exactly localized at the end sites. $U_p$ may be attractive or repulsive depending on other system parameters. We also give a qualitative understanding of the effect of interaction under the self-consistent mean field framework.

Quantum Quench Dynamics

NASA Astrophysics Data System (ADS)

Mitra, Aditi

2018-03-01

Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum quenches is reviewed. Quenches in interacting one-dimensional systems as well as systems in higher spatial dimensions are covered. The appearance of nontrivial steady states following a quench in exactly solvable models is discussed, and the stability of these states to perturbations is described. Proper conserving approximations needed to capture the onset of thermalization at long times are outlined. The appearance of universal scaling for quenches near critical points and the role of the renormalization group in capturing the transient regime are reviewed. Finally, the effect of quenches near critical points on the dynamics of entanglement entropy and entanglement statistics is discussed. The extraction of critical exponents from the entanglement statistics is outlined.

Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions

NASA Astrophysics Data System (ADS)

Pelissetto, Andrea; Rossini, Davide; Vicari, Ettore

2018-03-01

We investigate the quantum dynamics of many-body systems subject to local (i.e., restricted to a limited space region) time-dependent perturbations. If the system crosses a quantum phase transition, an off-equilibrium behavior is observed, even for a very slow driving. We show that, close to the transition, time-dependent quantities obey scaling laws. In first-order transitions, the scaling behavior is universal, and some scaling functions can be computed exactly. For continuous transitions, the scaling laws are controlled by the standard critical exponents and by the renormalization-group dimension of the perturbation at the transition. Our protocol can be implemented in existing relatively small quantum simulators, paving the way for a quantitative probe of the universal off-equilibrium scaling behavior, without the need to manipulate systems close to the thermodynamic limit.

The renormalization group and the implicit function theorem for amplitude equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirkinis, Eleftherios

2008-07-15

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen et al., Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation formore » both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases.« less

Renormalization of the unitary evolution equation for coined quantum walks

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan; Portugal, Renato

2017-03-01

We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.

Superconformal quantum field theory in curved spacetime

NASA Astrophysics Data System (ADS)

de Medeiros, Paul; Hollands, Stefan

2013-09-01

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer.

PubMed

Sharma, Sandeep

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10(12) many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a(3)Πu, b(3)Σg (-), A(1)Πu, c(3)Σu (+), B(1)Δg, B(') (1)Σg (+), d(3)Πg, and C(1)Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations (1)Σg (+), (1)Σu (+), (1)Σg (-), and (1)Σu (-), to an estimated accuracy of 0.1 mEh of the exact result in this basis.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

NASA Astrophysics Data System (ADS)

Sharma, Sandeep

2015-01-01

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X.

PubMed

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A; Sondhi, S L

2017-12-13

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A.; Sondhi, S. L.

2017-10-01

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

The use of effective variables in high energy physics

NASA Astrophysics Data System (ADS)

Baumgart, Matthew Todd

In high energy physics, we often gain by systematically reducing the formal description of a physical system or the data sets that come from particle colliders. Converting the naive, original setup results in a more useful set of couplings, fields, or observables, which we call effective variables. This thesis considers several examples of them: We take a φ4 scalar field theory and renormalize it according to the equations of Wilsonian exact renormalization group. Whatever the initial setup of the theory, this results in an infinite number of operators. We demonstrate a procedure to remove all interaction terms except for the quartic. We find its coupling has the same one-loop beta-function as obtained from standard renormalization group. We also examine the relationship between little Higgs and 5d composite models with identical symmetries. By performing an "extreme" deconstruction, one can reduce any warped composite model to a little Higgs theory on a handful of sites. We find that the finiteness of the Higgs potential in 5d is due to the same collective symmetry breaking as in the little Higgs. We compare a 4d and 5d model with the same symmetry to the data. We see that the 5d model has difficulty meeting several constraints simultaneously. By contrast, the Minimal Moose with custodial symmetry is viable in a large region of its parameter space. Finally, we turn our attentions to the hadron collider environment. In the context of SUSY extended by U(1)', production of an initial Z' gauge boson gives us an additional kinematic constraint. We use this to implement a novel method to measure all of the superpartner masses involved in its decay. For certain final states with two invisible particles, one can construct kinematic observables bounded above by parent particle masses. Additionally, we study other effects of extending the MSSM by a Z '. The production cross-section of sleptons is enhanced over the MSSM, so the discovery potential for sleptons is greatly increased. The flavor and charge information in the resulting slepton decay provides a useful handle on the identity of the LSP.

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.; Simms, R. M.

2018-04-01

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

Renormalization group analysis of dipolar Heisenberg model on square lattice

NASA Astrophysics Data System (ADS)

Keleş, Ahmet; Zhao, Erhai

2018-06-01

We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well-known J1-J2 model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here, we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phases. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range-ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

Renormalization group naturalness of GUT Higgs potentials

NASA Astrophysics Data System (ADS)

Allanach, B. C.; Amelino-Camelia, G.; Philipsen, O.; Pisanti, O.; Rosa, L.

1999-01-01

We analyze the symmetry-breaking patterns of grand unified theories from the point of view of a recently proposed criterion of renormalization-group naturalness. We perform the analysis on simple non-SUSY SU(5) and SO(10) and SUSY SU(5) GUTs. We find that the naturalness criterion can favor spontaneous symmetry breaking in the direction of the smallest of the maximal little groups. Some differences between theories with and without supersymmetry are also emphasized.

Covariant Derivatives and the Renormalization Group Equation

NASA Astrophysics Data System (ADS)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Renormalization group flow of the Higgs potential.

PubMed

Gies, Holger; Sondenheimer, René

2018-03-06

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

NASA Astrophysics Data System (ADS)

Giuliano, Domenico; Nava, Andrea

2015-09-01

Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within the bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.

Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

NASA Astrophysics Data System (ADS)

Aristov, D. N.; Wölfle, P.

2018-05-01

We develop the renormalization group theory of the conductances of N -lead junctions of spinless Luttinger-liquid wires as functions of bias voltages applied to N independent Fermi-liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group β functions are derived up to second order.

Emergent supersymmetry in the marginal deformations of $$\\mathcal{N}=4$$ SYM

DOE PAGES

Jin, Qingjun

2016-10-24

Here, we study the one loop renormalization group flow of the marginal deformations ofmore » $$\\mathcal{N}=4$$ SYM theory using the a-function. We found that in the planar limit some non-supersymmetric deformations flow to the supersymmetric infrared fixed points described by the Leigh-Strassler theory. This means supersymmetry emerges as a result of renormalization group flow.« less

Representation of Renormalization Group Functions By Nonsingular Integrals in a Model of the Critical Dynamics of Ferromagnets: The Fourth Order of The ɛ-Expansion

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts.; Vorob'eva, S. E.; Ivanova, E. V.; Kompaniets, M. V.

2018-04-01

Using the representation for renormalization group functions in terms of nonsingular integrals, we calculate the dynamical critical exponents in the model of critical dynamics of ferromagnets in the fourth order of the ɛ-expansion. We calculate the Feynman diagrams using the sector decomposition technique generalized to critical dynamics problems.

Quantum gravity and renormalization

NASA Astrophysics Data System (ADS)

Anselmi, Damiano

2015-02-01

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

Effective scalar field theory and reduction of couplings

NASA Astrophysics Data System (ADS)

Atance, Mario; Cortés, José Luis

1997-09-01

A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the possibility to go beyond the renormalizable φ4 theory without losing its predictive power. It is shown that there is a minimal extension with just one additional free parameter (the mass scale of the effective theory expansion) and some of its properties are discussed.

Callan-Symanzik equations for infrared Yang-Mills theory

NASA Astrophysics Data System (ADS)

Weber, Axel; Dall'Olio, Pietro

2017-12-01

Dyson-Schwinger equations have been successful in determining the correlation functions in Yang-Mills theory in the Landau gauge, in the infrared regime. We argue that similar results can be obtained, in a technically simpler way, with Callan-Symanzik renormalization group equations. We present generalizations of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011, and show how the renormalization scheme dependence can be used to improve the matching to the existing lattice data for the gluon and ghost propagators.

Renormalization Group scale-setting in astrophysical systems

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2011-09-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

Simple and Accurate Method for Central Spin Problems

NASA Astrophysics Data System (ADS)

Lindoy, Lachlan P.; Manolopoulos, David E.

2018-06-01

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long timescales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins. This method does not suffer from the statistical errors that accompany a Monte Carlo sampling of the exact eigenstates of the central spin Hamiltonian obtained from the algebraic Bethe ansatz, or from the growth of the truncation error with time in the time-dependent density matrix renormalization group (TDMRG) approach. As a result, it can be applied to larger central spin problems than the algebraic Bethe ansatz, and for longer times than the TDMRG algorithm. It is therefore an ideal method to use to solve central spin problems, and we expect that it will also prove useful for a variety of related problems that arise in a number of different research fields.

Quantum criticality and duality in the Sachdev-Ye-Kitaev/AdS2 chain

NASA Astrophysics Data System (ADS)

Jian, Shao-Kai; Xian, Zhuo-Yu; Yao, Hong

2018-05-01

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS2 chain. Specifically, by studying a double-trace deformation of a Z2 scalar in an AdS2 chain where the Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS2 chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS2 space-time.

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

DOE PAGES

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko; ...

2017-09-11

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.

We consider the sign problem for classical spin models at complexmore » $$\\beta =1/g_0^2$$ on $$L\\times L$$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$$\\beta$$ than the reweighting Monte Carlo method. For the Ising model with complex $$\\beta$$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $$L\\times L$$ lattices when the number of states $$D_s$$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.« less

Remarks on the renormalization group in statistical fluid dynamics

NASA Astrophysics Data System (ADS)

Fournier, J.-D.; Frisch, U.

1983-08-01

A variant of the renormalization group is applied to the problem of randomly forced fluids studied by Forster, Nelson, and Stephen

Fickian dispersion is anomalous

DOE PAGES

Cushman, John H.; O’Malley, Dan

2015-06-22

The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion wemore » illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify non-Fickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finite-size Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are p-self-similar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized self-similar processes. Finally, power-law clocks are introduced to examine multi-scaling behavior. Several examples of these ideas are presented and discussed.« less

Loop optimization for tensor network renormalization

NASA Astrophysics Data System (ADS)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Loop-corrected Virasoro symmetry of 4D quantum gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, T.; Kapec, D.; Raclariu, A.

Recently a boundary energy-momentum tensor T zz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an “anomaly” which is one-loop exact, T zz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts T zz .

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.

PubMed

Tsiper, E V

2006-08-18

The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.

Loop-corrected Virasoro symmetry of 4D quantum gravity

DOE PAGES

He, T.; Kapec, D.; Raclariu, A.; ...

2017-08-16

Recently a boundary energy-momentum tensor T zz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an “anomaly” which is one-loop exact, T zz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts T zz .

Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

NASA Astrophysics Data System (ADS)

Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei; Kawashima, Naoki; Sota, Shigetoshi; Tohyama, Takami; Imada, Masatoshi

2017-08-01

We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), 10.1103/PhysRevLett.113.107201], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid.

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

NASA Astrophysics Data System (ADS)

Connes, Alain; Kreimer, Dirk

This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

The density-matrix renormalization group: a short introduction.

PubMed

Schollwöck, Ulrich

2011-07-13

The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

PubMed

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke

We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.

Renormalization group analysis of B →π form factors with B -meson light-cone sum rules

NASA Astrophysics Data System (ADS)

Shen, Yue-Long; Wei, Yan-Bing; Lü, Cai-Dian

2018-03-01

Within the framework of the B -meson light-cone sum rules, we review the calculation of radiative corrections to the three B →π transition form factors at leading power in Λ /mb. To resum large logarithmic terms, we perform the complete renormalization group evolution of the correlation function. We employ the integral transformation which diagonalizes evolution equations of the jet function and the B -meson light-cone distribution amplitude to solve these evolution equations and obtain renormalization group improved sum rules for the B →π form factors. Results of the form factors are extrapolated to the whole physical q2 region and are compared with that of other approaches. The effect of B -meson three-particle light-cone distribution amplitudes, which will contribute to the form factors at next-to-leading power in Λ /mb at tree level, is not considered in this paper.

Leading temperature dependence of the conductance in Kondo-correlated quantum dots.

PubMed

Aligia, A A

2018-04-18

Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

Transient and Sharvin resistances of Luttinger liquids

NASA Astrophysics Data System (ADS)

Kloss, Thomas; Weston, Joseph; Waintal, Xavier

2018-04-01

Although the intrinsic conductance of an interacting one-dimensional system is renormalized by the electron-electron correlations, it has been known for some time that this renormalization is washed out by the presence of the (noninteracting) electrodes to which the wire is connected. Here, we study the transient conductance of such a wire: a finite voltage bias is suddenly applied across the wire and we measure the current before it has enough time to reach its stationary value. These calculations allow us to extract the Sharvin (contact) resistance of Luttinger and Fermi liquids. In particular, we find that a perfect junction between a Fermi liquid electrode and a Luttinger liquid electrode is characterized by a contact resistance that consists of half the quantum of conductance in series with half the intrinsic resistance of an infinite Luttinger liquid. These results were obtained using two different methods: a dynamical Hartree-Fock approach and a self-consistent Boltzmann approach. Although these methods are formally approximate, we find a perfect match with the exact results of Luttinger/Fermi liquid theory.

Focus on quantum Einstein gravity Focus on quantum Einstein gravity

NASA Astrophysics Data System (ADS)

Ambjorn, Jan; Reuter, Martin; Saueressig, Frank

2012-09-01

The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishing quantum Einstein gravity as a fundamental theory of gravity, without introducing supersymmetry or extra dimensions, and solely based on quantization techniques that are known to work well for the other fundamental forces of nature. While the idea of gravity being asymptotically safe was proposed by Steven Weinberg more than 30 years ago [1], the technical tools for investigating this scenario only emerged during the last decade. Here a key role is played by the exact functional renormalization group equation for gravity, which allows the construction of non-perturbative approximate solutions for the RG-flow of the gravitational couplings. Most remarkably, all solutions constructed to date exhibit a suitable non-Gaussian fixed point, lending strong support to the asymptotic safety conjecture. Moreover, the functional renormalization group also provides indications that the central idea of a non-Gaussian fixed point providing a safe ultraviolet completion also carries over to more realistic scenarios where gravity is coupled to a suitable matter sector like the standard model. These theoretical successes also triggered a wealth of studies focusing on the consequences of asymptotic safety in a wide range of phenomenological applications covering the physics of black holes, early time cosmology and the big bang, as well as TeV-scale gravity models testable at the Large Hadron Collider. On different grounds, Monte-Carlo studies of the gravitational partition function based on the discrete causal dynamical triangulations approach provide an a priori independent avenue towards unveiling the non-perturbative features of gravity. As a highlight, detailed simulations established that the phase diagram underlying causal dynamical triangulations contains a phase where the triangulations naturally give rise to four-dimensional, macroscopic universes. Moreover, there are indications for a second-order phase transition that naturally forms the discrete analog of the non-Gaussian fixed point seen in the continuum computations. Thus there is a good chance that the discrete and continuum computations will converge to the same fundamental physics. This focus issue collects a series of papers that outline the current frontiers of the gravitational asymptotic safety program. We hope that readers get an impression of the depth and variety of this research area as well as our excitement about the new and ongoing developments. References [1] Weinberg S 1979 General Relativity, an Einstein Centenary Survey ed S W Hawking and W Israel (Cambridge: Cambridge University Press)

Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Drivas, Theodore D.

2018-02-01

We develop a first-principles theory of relativistic fluid turbulence at high Reynolds and Péclet numbers. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. We obtain results very similar to those for nonrelativistic turbulence, with hydrodynamic fields in the inertial range described as distributional or "coarse-grained" solutions of the relativistic Euler equations. These solutions do not, however, satisfy the naive conservation laws of smooth Euler solutions but are afflicted with dissipative anomalies in the balance equations of internal energy and entropy. The anomalies are shown to be possible by exactly two mechanisms, local cascade and pressure-work defect. We derive "4 /5 th-law" type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required for their not vanishing. We also investigate the Lorentz covariance of the inertial-range fluxes, which we find to be broken by our coarse-graining regularization but which is restored in the limit where the regularization is removed, similar to relativistic lattice quantum field theory. In the formal limit as speed of light goes to infinity, we recover the results of previous nonrelativistic theory. In particular, anomalous heat input to relativistic internal energy coincides in that limit with anomalous dissipation of nonrelativistic kinetic energy.

Relation between random walks and quantum walks

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Falkner, Stefan; Portugal, Renato

2015-05-01

Based on studies of four specific networks, we conjecture a general relation between the walk dimensions dw of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that dw of the quantum walk takes on exactly half the value found for the classical random walk on the same geometry. Since walks on homogeneous lattices satisfy this relation trivially, our results for heterogeneous networks suggest that such a relation holds irrespective of whether translational invariance is maintained or not. To develop our results, we extend the renormalization-group analysis (RG) of the stochastic master equation to one with a unitary propagator. As in the classical case, the solution ρ (x ,t ) in space and time of this quantum-walk equation exhibits a scaling collapse for a variable xdw/t in the weak limit, which defines dw and illuminates fundamental aspects of the walk dynamics, e.g., its mean-square displacement. We confirm the collapse for ρ (x ,t ) in each case with extensive numerical simulation. The exact values for dw themselves demonstrate that RG is a powerful complementary approach to study the asymptotics of quantum walks that weak-limit theorems have not been able to access, such as for systems lacking translational symmetries beyond simple trees.

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-10-01

In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015), 10.1103/PhysRevE.91.013002] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n , all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E ∝k⊥1 -ξ and the dispersion law ω ∝k⊥2 -η . In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale L .

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

Renormalization group procedure for potential -g/r2

NASA Astrophysics Data System (ADS)

Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.

2018-02-01

Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

NASA Astrophysics Data System (ADS)

Antenucci, F.; Crisanti, A.; Leuzzi, L.

2014-07-01

The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

Exploration of quantum phases transition in the XXZ model with Dzyaloshinskii-Moriya interaction using trance distance discord

NASA Astrophysics Data System (ADS)

Zhang, Ren-jie; Xu, Shuai; Shi, Jia-dong; Ma, Wen-chao; Ye, Liu

2015-11-01

In the paper, we researched the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group (QRG) method. The innovation point is that we adopt a new approach called trace distance discord to indicate the quantum correlation of the system. QPT after several iterations of renormalization in current system has been observed. Consequently, it opened the possibility of investigation of QPR in the geometric discord territory. While the anisotropy suppresses the correlation due to favoring of the alignment of spins, the DM interaction restores the spoiled correlation via creation of the quantum fluctuations. We also apply quantum renormalization group method to probe the thermodynamic limit of the model and emerging of nonanalytic behavior of the correlation.

Critical behavior of a chiral superfluid in a bipartite square lattice

NASA Astrophysics Data System (ADS)

Okamoto, Junichi; Huang, Wen-Min; Höppner, Robert; Mathey, Ludwig

2018-01-01

We study the critical behavior of Bose-Einstein condensation in the second band of a bipartite optical square lattice in a renormalization group framework at one-loop order. Within our field theoretical representation of the system, we approximate the system as a two-component Bose gas in three dimensions. We demonstrate that the system is in a different universality class than the previously studied condensation in a frustrated triangular lattice due to an additional Umklapp scattering term, which stabilizes the chiral superfluid order at low temperatures. We derive the renormalization group flow of the system and show that this order persists in the low energy limit. Furthermore, the renormalization flow suggests that the phase transition from the thermal phase to the chiral superfluid state is first order.

Development of a Renormalization Group Approach to Multi-Scale Plasma Physics Computation

DTIC Science & Technology

2012-03-28

with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1...NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: a . REPORT...code) 29-12-2008 Final Technical Report From 29-12-2008 To 16-95-2011 (STTR PHASE II) DEVELOPMENT OF A RENORMALIZATION GROUP APPROACH TO MULTI-SCALE

New applications of renormalization group methods in nuclear physics.

PubMed

Furnstahl, R J; Hebeler, K

2013-12-01

We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

Renormalization Group Theory for the Imbalanced Fermi Gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gubbels, K. B.; Stoof, H. T. C.

2008-04-11

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)].

Application of renormalization group theory to the large-eddy simulation of transitional boundary layers

NASA Technical Reports Server (NTRS)

Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.

1990-01-01

An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

The long flow to freedom

DOE PAGES

Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan; ...

2017-02-10

Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N = (2,2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one)more » and a non-zero Fayet-Iliopoulos term, and pure SU( N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. As a result, we expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.« less

Kenneth Wilson and Renormalization

Science.gov Websites

of the Renormalization Group (RG) into a central tool in physics. ... He received a doctorate from one of the most amazing experiences of my life," says Peskin. "He was saying, 'I see the big actually the data you need to move from one scale to another. ... RG theory implies that, with enough

Renormalizable group field theory beyond melonic diagrams: An example in rank four

NASA Astrophysics Data System (ADS)

Carrozza, Sylvain; Lahoche, Vincent; Oriti, Daniele

2017-09-01

We prove the renormalizability of a gauge-invariant, four-dimensional group field theory (GFT) model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories. We also explore the renormalization group flow of the model at the nonperturbative level, using functional renormalization group methods, and identify a nontrivial fixed point in various truncations. This model is expected to have a similar structure of divergences as the GFT models of 4D quantum gravity, thus paving the way to more detailed investigations on them.

Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gu Zhengcheng; Wen Xiaogang

2009-10-15

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors T{sub inv} plus the symmetry group G{sub sym} of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, asmore » illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (G{sub sym},T{sub inv}) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (G{sub sym},T{sub inv}) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.« less

Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

NASA Astrophysics Data System (ADS)

Rusin, Tomasz M.; Zawadzki, Wlodek

2018-05-01

Friedel oscillations (FO) of electron density caused by a deltalike neutral impurity in two-dimensional (2D) systems in a magnetic field are calculated. Three 2D cases are considered: free electron gas, monolayer graphene, and group-VI dichalcogenides. An exact form of the renormalized Green's function is used in the calculations, as obtained by a summation of the infinite Dyson series and regularization procedure. Final results are valid for large ranges of potential strengths V0, electron densities ne, magnetic fields B , and distances from the impurity r . Realistic models for the impurities are used. The first FO of induced density in WS2 are described by the relation Δ n (r ) ∝sin(2 π r /TFO) /r2 , where TFO∝1 /√{EF} . For weak impurity potentials, the amplitudes of FO are proportional to V0. For attractive potentials and high fields, the total electron density remains positive for all r . On the other hand, for low fields, repulsive potentials and small r , the total electron density may become negative, so that many-body effects should be taken into account.

The B - L/electroweak Hierarchy in Smooth Heterotic Compactifications

NASA Astrophysics Data System (ADS)

Ambroso, Michael; Ovrut, Burt A.

E8 × E8 heterotic string and M-theory, when appropriately compactified, can give rise to realistic, N = 1 supersymmetric particle physics. In particular, the exact matter spectrum of the MSSM, including three right-handed neutrino supermultiplets, one per family, and one pair of Higgs-Higgs conjugate superfields is obtained by compactifying on Calabi-Yau manifolds admitting specific SU(4) vector bundles. These "heterotic standard models" have the SU(3)C × SU(2)L × U(1)Y gauge group of the standard model augmented by an additional gauged U(1)B - L. Their minimal content requires that the B - L gauge symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. In a previous paper, we presented the results of a renormalization group analysis showing that B - L gauge symmetry is indeed radiatively broken with a B - L/electroweak hierarchy of { O}(10) to { O}(102). In this paper, we present the details of that analysis, extending the results to include higher order terms in tan β-1 and the explicit spectrum of all squarks and sleptons.

New applications of the renormalization group method in physics: a brief introduction.

PubMed

Meurice, Y; Perry, R; Tsai, S-W

2011-07-13

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

Multiloop Functional Renormalization Group That Sums Up All Parquet Diagrams

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present a multiloop flow equation for the four-point vertex in the functional renormalization group (FRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of FRG computations for the four-point vertex and, consequently, the self-energy. Using the x-ray-edge singularity as an example, we show that solving the multiloop FRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.

A general non-Abelian density matrix renormalization group algorithm with application to the C{sub 2} dimer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharma, Sandeep, E-mail: sanshar@gmail.com

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve ofmore » the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.« less

EDITORIAL: Focus on Quantum Information and Many-Body Theory

NASA Astrophysics Data System (ADS)

Eisert, Jens; Plenio, Martin B.

2010-02-01

Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac and F Verstraete SIMULATION AND DYNAMICS A quantum differentiation of k-SAT instances B Tamir and G Ortiz Classical Ising model test for quantum circuits Joseph Geraci and Daniel A Lidar Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain S R Clark, J Prior, M J Hartmann, D Jaksch and M B Plenio Exact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition Tomaž Prosen and Bojan Žunkovič Quantum kinetic Ising models R Augusiak, F M Cucchietti, F Haake and M Lewenstein ENTANGLEMENT AND SPECTRAL PROPERTIES Ground states of unfrustrated spin Hamiltonians satisfy an area law Niel de Beaudrap, Tobias J Osborne and Jens Eisert Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group W Münder, A Weichselbaum, A Holzner, Jan von Delft and C L Henley The invariant-comb approach and its relation to the balancedness of multipartite entangled states Andreas Osterloh and Jens Siewert Entanglement scaling of fractional quantum Hall states through geometric deformations Andreas M Läuchli, Emil J Bergholtz and Masudul Haque Entanglement versus gap for one-dimensional spin systems Daniel Gottesman and M B Hastings Entanglement spectra of critical and near-critical systems in one dimension F Pollmann and J E Moore Macroscopic bound entanglement in thermal graph states D Cavalcanti, L Aolita, A Ferraro, A García-Saez and A Acín Entanglement at the quantum phase transition in a harmonic lattice Elisabeth Rieper, Janet Anders and Vlatko Vedral Multipartite entanglement and frustration P Facchi, G Florio, U Marzolino, G Parisi and S Pascazio Entropic uncertainty relations—a survey Stephanie Wehner and Andreas Winter Entanglement in a spin system with inverse square statistical interaction D Giuliano, A Sindona, G Falcone, F Plastina and L Amico APPLICATIONS Time-dependent currents of one-dimensional bosons in an optical lattice J Schachenmayer, G Pupillo and A J Daley Implementing quantum gates using the ferromagnetic spin-J XXZ chain with kink boundary conditions Tom Michoel, Jaideep Mulherkar and Bruno Nachtergaele Long-distance entanglement in many-body atomic and optical systems Salvatore M Giampaolo and Fabrizio Illuminati QUANTUM MEMORIES AND TOPOLOGICAL ORDER Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes Stefano Chesi, Daniel Loss, Sergey Bravyi and Barbara M Terhal Topological color codes and two-body quantum lattice Hamiltonians M Kargarian, H Bombin and M A Martin-Delgado RENORMALIZATION Local renormalization method for random systems O Gittsovich, R Hübener, E Rico and H J Briegel

Two-loop renormalization of gaugino masses in general supersymmetric gauge models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamada, Y.

1994-01-03

We calculate the two-loop renormalization group equations for the running gaugino masses in general supersymmetry (SUSY) gauge models, improving our previous result. We also study its consequences on the unification of the gaugino masses in the SUSY SU(5) model. The two-loop correction to the one-loop relation [ital m][sub [ital i

Critical Exponents, Scaling Law, Universality and Renormalization Group Flow in Strong Coupling QED

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi

The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katanin, A. A., E-mail: katanin@mail.ru

We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32].more » We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.« less

Impact of topology in foliated quantum Einstein gravity.

PubMed

Houthoff, W B; Kurov, A; Saueressig, F

2017-01-01

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

Phase structure of NJL model with weak renormalization group

NASA Astrophysics Data System (ADS)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Restoration of dimensional reduction in the random-field Ising model at five dimensions

NASA Astrophysics Data System (ADS)

Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Restoration of dimensional reduction in the random-field Ising model at five dimensions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review.

PubMed

Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin

2015-12-01

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme--this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the 'principle of minimum sensitivity' (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R(e+e-) and [Formula: see text] up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice of initial scale is highly suppressed even for low-order predictions. Thus the PMC, based on the standard RGI, has a rigorous foundation; it eliminates an unnecessary systematic error for high precision pQCD predictions and can be widely applied to virtually all high-energy hadronic processes, including multi-scale problems.

Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

NASA Astrophysics Data System (ADS)

Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

2015-12-01

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice of initial scale is highly suppressed even for low-order predictions. Thus the PMC, based on the standard RGI, has a rigorous foundation; it eliminates an unnecessary systematic error for high precision pQCD predictions and can be widely applied to virtually all high-energy hadronic processes, including multi-scale problems.

A key heterogeneous structure of fractal networks based on inverse renormalization scheme

NASA Astrophysics Data System (ADS)

Bai, Yanan; Huang, Ning; Sun, Lina

2018-06-01

Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

Alien calculus and a Schwinger-Dyson equation: two-point function with a nonperturbative mass scale

NASA Astrophysics Data System (ADS)

Bellon, Marc P.; Clavier, Pierre J.

2018-02-01

Starting from the Schwinger-Dyson equation and the renormalization group equation for the massless Wess-Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.

2PI effective theory at next-to-leading order using the functional renormalization group

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Friesen, S. A.; Meggison, B. A.; Phillips, C. D.; Pickering, D.; Sohrabi, K.

2018-02-01

We consider a symmetric scalar theory with quartic coupling in four dimensions. We show that the four-loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.

Topological Luttinger liquids from decorated domain walls

NASA Astrophysics Data System (ADS)

Parker, Daniel E.; Scaffidi, Thomas; Vasseur, Romain

2018-04-01

We introduce a systematic construction of a gapless symmetry-protected topological phase in one dimension by "decorating" the domain walls of Luttinger liquids. The resulting strongly interacting phases provide a concrete example of a gapless symmetry-protected topological (gSPT) phase with robust symmetry-protected edge modes. Using boundary conformal field theory arguments, we show that while the bulks of such gSPT phases are identical to conventional Luttinger liquids, their boundary critical behavior is controlled by a different, strongly coupled renormalization group fixed point. Our results are checked against extensive density matrix renormalization group calculations.

Exploring excited eigenstates of many-body systems using the functional renormalization group

NASA Astrophysics Data System (ADS)

Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph

2018-05-01

We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.

Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Sheng-Quan; Wu, Xing-Gang; Brodsky, Stanley J.

We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice overmore » the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m H = 125 GeV , the PMC predictions for the p p → H X Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are σ Incl | 7 TeV = 21.2 1 + 1.36 - 1.32 pb , σ Incl | 8 TeV = 27.3 7 + 1.65 - 1.59 pb , and σ Incl | 13 TeV = 65.7 2 + 3.46 - 3.0 pb . We also predict the fiducial cross section σ fid ( p p → H → γ γ ) : σ fid | 7 TeV = 30.1 + 2.3 - 2.2 fb , σ fid | 8 TeV = 38.3 + 2.9 - 2.8 fb , and σ fid | 13 TeV = 85.8 + 5.7 - 5.3 fb . The error limits in these predictions include the small residual high-order renormalization-scale dependence plus the uncertainty from the factorization scale. The PMC predictions show better agreement with the ATLAS measurements than the LHC Higgs Cross Section Working Group predictions which are based on conventional renormalization-scale setting.« less

Bulk renormalization and particle spectrum in codimension-two brane worlds

NASA Astrophysics Data System (ADS)

Salvio, Alberto

2013-04-01

We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).

Self-interacting polymer chains terminally anchored to adsorbing surfaces of three-dimensional fractal lattices

NASA Astrophysics Data System (ADS)

Živić, I.; Elezović-Hadžić, S.; Milošević, S.

2018-01-01

We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

Entanglement in the Anisotropic Kondo Necklace Model

NASA Astrophysics Data System (ADS)

Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Xue-ke; Wu, Tao; Xu, Shuai

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strongmore » enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.« less

Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

NASA Astrophysics Data System (ADS)

Pixley, J. H.; Cole, William S.; Spielman, I. B.; Rizzi, Matteo; Das Sarma, S.

2017-10-01

We study the odd-integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a universality class with critical exponents associated with the divergence of the correlation length ν ≈2 /3 and the order-parameter susceptibility γ ≈1 /2 . We solve the effective spin model exactly using the density-matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

Anomalous diffusion on the Hanoi networks

NASA Astrophysics Data System (ADS)

Boettcher, S.; Gonçalves, B.

2008-11-01

Diffusion is modeled on the recently proposed Hanoi networks by studying the mean-square displacement of random walks with time, langr2rang~t2/dw. It is found that diffusion —the quintessential mode of transport throughout Nature— proceeds faster than ordinary, in one case with an exact, anomalous exponent dw=2- log2(phi)=1.30576... . It is an instance of a physical exponent containing the "golden ratio"\\phi=(1+\\sqrt{5})/2 that is intimately related to Fibonacci sequences and since Euclid's time has been found to be fundamental throughout geometry, architecture, art, and Nature itself. It originates from a singular renormalization group fixed point with a subtle boundary layer, for whose resolution phi is the main protagonist. The origin of this rare singularity is easily understood in terms of the physics of the process. Yet, the connection between network geometry and the emergence of phi in this context remains elusive. These results provide an accurate test of recently proposed universal scaling forms for first passage times.

Interacting preformed Cooper pairs in resonant Fermi gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gubbels, K. B.; Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, NL-6525 AJ Nijmegen; Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht

2011-07-15

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozieres-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalismmore » with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi et al. [Science 327, 442 (2010)] and Nascimbene et al. [Nature (London) 463, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, which can be tested in experiments.« less

Flat electronic bands in fractal-kagomé network and the effect of perturbation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandy, Atanu, E-mail: atanunandy1989@gmail.com; Chakrabarti, Arunava, E-mail: arunava-chakrabarti@yahoo.co.in

2016-05-06

We demonstrate an analytical prescription of demonstrating the flat band [FB] states in a fractal incorporated kagomé type network that can give rise to a countable infinity of flat non-dispersive eigenstates with a multitude of localization area. The onset of localization can, in principle, be delayed in space by an appropriate choice of energy regime. The length scale, at which the onset of localization for each mode occurs, can be tuned at will following the formalism developed within the framework of real space renormalization group. This scheme leads to an exact determination of energy eigenvalue for which one can havemore » dispersionless flat electronic bands. Furthermore, we have shown the effect ofuniform magnetic field for the same non-translationally invariant network model that has ultimately led to an‘apparent invisibility’ of such staggered localized states and to generate absolutely continuous sub-bands in the energy spectrum and again an interesting re-entrant behavior of those FB states.« less

Universality for shape dependence of Casimir effects from Weyl anomaly

NASA Astrophysics Data System (ADS)

Miao, Rong-Xin; Chu, Chong-Sun

2018-03-01

We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We also test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic models, we reproduce not only the precise form of the near boundary divergent behavior of the stress tensor, but also the surface counter term that is needed to make the total energy finite. As they are proportional to the central charges, the near boundary divergence of the stress tensor must be physical and cannot be dropped by further artificial renormalization. Our results thus provide affirmative support on the physical nature of the divergent energy density near the boundary, whose reality has been a long-standing controversy in the literature.

Critical frontier of the triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Qian, Xiaofeng; Wegewijs, Maarten; Blöte, Henk W.

2004-03-01

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.

Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network

NASA Astrophysics Data System (ADS)

Xie, Pinchen; Yang, Bingjia; Zhang, Zhongzhi; Andrade, Roberto F. S.

2018-07-01

A deterministic network with tree structure is considered, for which the spectrum of its adjacency matrix can be exactly evaluated by a recursive renormalization approach. It amounts to successively increasing number of contributions at any finite step of construction of the tree, resulting in a causal chain. The resulting eigenvalues can be related the full energy spectrum of a nearest-neighbor tight-binding model defined on this structure. Given this association, it turns out that further properties of the eigenvectors can be evaluated, like the degree of quantum localization of the tight-binding eigenstates, expressed by the inverse participation ratio (IPR). It happens that, for the current model, the IPR's are also suitable to be analytically expressed in terms in corresponding eigenvalue chain. The resulting IPR scaling behavior is expressed by the tails of eigenvalue chains as well.

Spatial correlations in driven-dissipative photonic lattices

NASA Astrophysics Data System (ADS)

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E.; Schmidt, Sebastian

2017-12-01

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array (∼ 1/z) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

2010-11-01

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

Frustrated S = 1/2 Two-Leg Ladder with Different Leg Interactions

NASA Astrophysics Data System (ADS)

Tonegawa, Takashi; Okamoto, Kiyomi; Hikihara, Toshiya; Sakai, Tôru

2017-04-01

We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J1,a and J1,b between nearest neighbor spins in the legs a and b, respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by Jr and ΔJr, respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J1,aJ1,b < 0 irrespective of the sign of Jr. The phase diagrams on the Δ (0≤Δ<1) versus J1,b plane in the cases of J1,a = - 0.2 and J1,a = 0.2 with Jr = -1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state, when J1,a + J1,b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.

Apker Award Recipient: Renormalization-Group Study of Helium Mixtures Immersed in a Porous Medium

NASA Astrophysics Data System (ADS)

Lopatnikova, Anna

1998-03-01

Superfluidity and phase separation in ^3He-^4He mixtures immersed in aerogel are studied by renormalization-group theory. Firstly, the theory is applied to jungle-gym (non-random) aerogel.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 55, 3798 (1997).) This calculation is conducted via the coupled renormalization-group mappings of interactions near and away from aerogel. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfludity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. Secondly, the theory is applied to true aerogel, which has quenched disorder at both atomic and geometric levels.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 56, 11865 (1997).) This calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of quenched probability distributions of random interactions. Random-bond effects on superfluidity onset and random-field effects on superfluid phase separation are seen. The quenched randomness causes the λ line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general prediction and experiments. Based on these studies, the experimentally observed(S.B. Kim, J. Ma, and M.H.W. Chan, Phys. Rev. Lett. 71, 2268 (1993); N. Mulders and M.H.W. Chan, Phys. Rev. Lett. 75, 3705 (1995).) distinctive characteristics of ^3He-^4He mixtures in aerogel are related to the aerogel properties of connectivity, tenuousness, and atomic and geometric randomness.

Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Hong -Hao; Wu, Xing -Gang; Ma, Yang

A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach tomore » all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R e+e– at four-loop order in pQCD.« less

Calculational Schemes in GUTs

NASA Astrophysics Data System (ADS)

Kounnas, Costas

The following sections are included: * Introduction * Mass Spectrum in a Spontaneously Broken-Theory SU(5) - Minimal Model * Renormalization and Renormalization Group Equation (R.G.E.) * Step Approximation and Decoupling Theorem * Notion of the Effective Coupling Constant * First Estimation of MX, α(MX) and sin2θ(MW) * Renormalization Properties and Photon-Z Mixing * β-Function Definitions * Threshold Functions and Decoupling Theorem * MX-Determination * Proton Lifetime * sin2θ(μ)-Determination * Quark-Lepton Mass Relations (mb/mτ) * Overview of the Conventional GUTs - Hierarchy Problem * Stability of Hierarchy - Supersymmetric GUTS * Cosmologically Acceptable SUSY GUT Models * Radiative Breaking of SU(2) × U(1) — MW/MX Hierarchy Generation * No Scale Supergravity Models^{56,57} Dynamical Determination of M_{B}-M_{F} * Conclusion * References

Continuum limit of Bk from 2+1 flavor domain wall QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soni, A.; T. Izubuchi, et al.

2011-07-01

We determine the neutral kaon mixing matrix element B{sub K} in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing. We introduce a significant improvement to the conventional nonperturbative renormalization (NPR) method in which the bare matrix elements are renormalized nonperturbatively in the regularization invariant momentum scheme (RI-MOM) and are then converted into the MS{sup -} scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four nonexceptional intermediate momentum schemesmore » that suppress infrared nonperturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of regularization invariant symmetric momentum schemes (RI-SMOM) and MS{sup -} at one-loop order. Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit. We control chiral extrapolation errors by considering both the next-to-leading order SU(2) chiral effective theory, and an analytic mass expansion. We obtain B{sub K}{sup MS{sup -}} (3 GeV) = 0.529(5){sub stat}(15){sub {chi}}(2){sub FV}(11){sub NPR}. This corresponds to B{sup -}{sub K}{sup RGI{sup -}} = 0.749(7){sub stat}(21){sub {chi}}(3){sub FV}(15){sub NPR}. Adding all sources of error in quadrature, we obtain B{sup -}{sub K}{sup RGI{sup -}} = 0.749(27){sub combined}, with an overall combined error of 3.6%.« less

A unified effective-field renormalization-group framework approach for the quenched diluted Ising models

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Fittipaldi, I. P.

1994-05-01

A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.

Ward identities and chiral anomalies for coupled fermionic chains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, L. C.; Ferraz, A.; Mastropietro, Vieri

2013-12-15

Coupled fermionic chains are usually described by an effective model written in terms of bonding and anti-bonding fermionic fields with linear dispersion in the vicinities of the respective Fermi points. We derive for the first time exact Ward Identities (WI) for this model, proving the existence of chiral anomalies which verify the Adler-Bardeen non-renormalization property. Such WI are expected to play a crucial role in the understanding of the thermodynamic properties of the system. Our results are non-perturbative and are obtained analyzing Grassmann functional integrals by means of constructive quantum field theory methods.

Higher-order quantum-chromodynamic corrections to the longitudinal coefficient function in deep-inelastic scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sowell, G.A.

1982-01-01

A calculation of nonsinglet longitudinal coefficient function of deep-inelastic scattering through order-g/sup 4/ is presented, using the operator-product expansion and the renormalization group. Both ultraviolet and infrared divergences are regulated with dimensional regularization. The renormalization scheme dependence of the result is discussed along with its phenomenological application in the determination of R = sigma/sub L//sigma/sub T/.

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

NASA Astrophysics Data System (ADS)

Nakatani, Naoki; Chan, Garnet Kin-Lic

2013-04-01

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

The Renormalization-Group Method in the Problem on Calculation of the Spectral Energy Density of Fluid Turbulence

NASA Astrophysics Data System (ADS)

Teodorovich, E. V.

2018-03-01

In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2018-05-01

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

Improving the In-Medium Similarity Renormalization Group via approximate inclusion of three-body effects

NASA Astrophysics Data System (ADS)

Morris, Titus; Bogner, Scott

2015-10-01

The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully not only to several closed shell finite nuclei, but has recently been used to produce effective shell model interactions that are competitive with phenomenological interactions in the SD shell. A recent alternative method for solving of the IM-SRG equations, called the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.

Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert

1994-01-01

Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

Renormalization-group study of superfluidity and phase separation of helium mixtures immersed in a nonrandom aerogel

NASA Astrophysics Data System (ADS)

Lopatnikova, Anna; Nihat Berker, A.

1997-02-01

Superfluidity and phase separation in 3-4He mixtures immersed in a jungle-gym (nonrandom) aerogel are studied by renormalization-group theory. Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low 4He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena and trends with respect to aerogel concentration are explained by the connectivity and tenuousness of a jungle-gym aerogel.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

NASA Astrophysics Data System (ADS)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

Importance of proper renormalization scale-setting for QCD testing at colliders

DOE PAGES

Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.

2015-12-22

A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. Furthermore, these results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.« less

Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations.

PubMed

Ding, Mingnan; Lu, Bing-Sui; Xing, Xiangjun

2016-10-01

Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

On the soft supersymmetry-breaking parameters in gauge-mediated models

NASA Astrophysics Data System (ADS)

Wagner, C. E. M.

1998-09-01

Gauge mediation of supersymmetry breaking in the observable sector is an attractive idea, which naturally alleviates the flavor changing neutral current problem of supersymmetric theories. Quite generally, however, the number and quantum number of the messengers are not known; nor is their characteristic mass scale determined by the theory. Using the recently proposed method to extract supersymmetry-breaking parameters from wave-function renormalization, we derived general formulae for the soft supersymmetry-breaking parameters in the observable sector, valid in the small and moderate tan β regimes, for the case of split messengers. The full leading-order effects of top Yukawa and gauge couplings on the soft supersymmetry-breaking parameters are included. We give a simple interpretation of the general formulae in terms of the renormalization group evolution of the soft supersymmetry-breaking parameters. As a by-product of this analysis, the one-loop renormalization group evolution of the soft supersymmetry-breaking parameters is obtained for arbitrary boundary conditions of the scalar and gaugino mass parameters at high energies.

Renormalization group study of the melting of a two-dimensional system of collapsing hard disks

NASA Astrophysics Data System (ADS)

Ryzhov, V. N.; Tareyeva, E. E.; Fomin, Yu. D.; Tsiok, E. N.; Chumakov, E. S.

2017-06-01

We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.

E-cigarette marketing and older smokers: road to renormalization.

PubMed

Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

2015-05-01

To describe older smokers' perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking.

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Renormalization Group Studies and Monte Carlo Simulation for Quantum Spin Systems.

NASA Astrophysics Data System (ADS)

Pan, Ching-Yan

We have discussed the extended application of various real space renormalization group methods to the quantum spin systems. At finite temperature, we extended both the reliability and range of application of the decimation renormalization group method (DRG) for calculating the thermal and magnetic properties of low-dimensional quantum spin chains, in which we have proposed general models of the three-state Potts model and the general Heisenberg model. Some interesting finite-temperature behavior of the models has been obtained. We also proposed a general formula for the critical properties of the n-dimensional q-state Potts model by using a modified migdal-Kadanoff approach which is in very good agreement with all available results for general q and d. For high-spin systems, we have investigated the famous Haldane's prediction by using a modified block renormalization group approach in spin -1over2, spin-1 and spin-3 over2 cases. Our result supports Haldane's prediction and a novel property of the spin-1 Heisenberg antiferromagnet has been predicted. A modified quantum monte Carlo simulation approach has been developed in this study which we use to treat quantum interacting problems (we only work on quantum spin systems in this study) without the "negative sign problem". We also obtain with the Monte Carlo approach the numerical derivative directly. Furthermore, using this approach we have obtained the energy spectrum and the thermodynamic properties of the antiferromagnetic q-state Potts model, and have studied the q-color problem with the result which supports Mattis' recent conjecture of entropy for the n -dimensional q-state Potts antiferromagnet. We also find a general solution for the q-color problem in d dimensions.

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

NASA Astrophysics Data System (ADS)

Tarpin, Malo; Canet, Léonie; Wschebor, Nicolás

2018-05-01

In this paper, we present theoretical results on the statistical properties of stationary, homogeneous, and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the non-perturbative renormalization group, we derive a closed renormalization flow equation for a generic n-point correlation (and response) function for large wave-numbers with respect to the inverse integral scale. The closure is obtained from a controlled expansion and relies on extended symmetries of the Navier-Stokes field theory. It yields the exact leading behavior of the flow equation at large wave-numbers |p→ i| and for arbitrary time differences ti in the stationary state. Furthermore, we obtain the form of the general solution of the corresponding fixed point equation, which yields the analytical form of the leading wave-number and time dependence of n-point correlation functions, for large wave-numbers and both for small ti and in the limit ti → ∞. At small ti, the leading contribution at large wave-numbers is logarithmically equivalent to -α (ɛL ) 2 /3|∑tip→ i|2, where α is a non-universal constant, L is the integral scale, and ɛ is the mean energy injection rate. For the 2-point function, the (tp)2 dependence is known to originate from the sweeping effect. The derived formula embodies the generalization of the effect of sweeping to n-point correlation functions. At large wave-numbers and large ti, we show that the ti2 dependence in the leading order contribution crosses over to a |ti| dependence. The expression of the correlation functions in this regime was not derived before, even for the 2-point function. Both predictions can be tested in direct numerical simulations and in experiments.

Role of fluctuations in random compressible systems at marginal dimensionality

NASA Astrophysics Data System (ADS)

Meissner, G.; Sasvári, L.; Tadić, B.

1986-07-01

In a unified treatment we have studied the role of fluctuations in uniaxial random systems at marginal dimensionality d*=4 with the n=1 component order parameter being coupled to elastic degrees of freedom. Depending on the ratio of the nonuniversal parameters of quenched disorder Δ0 and of elastic fluctuations v~0, a first- or second-order phase transition is found to occur, separated by a tricritical point. A complete account of critical properties and of macroscopic as well as of microscopic elastic stability is given for temperatures T>Tc. Universal singularities of thermodynamic functions are determined for t=(T-Tc)/Tc-->0 including the tricritical point: for v~0/Δ0>-2, they are the same as in a rigid random system; for v~0/Δ0=-2, they are different due to lattice compressibility being related, however, to the former by Fisher renormalization. Fluctuation corrections in one-loop approximation have been evaluated in a nonuniversal critical temperature range, tx<

Analysis of coined quantum walks with renormalization

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan

2018-01-01

We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

Renormalization of Supersymmetric QCD on the Lattice

NASA Astrophysics Data System (ADS)

Costa, Marios; Panagopoulos, Haralambos

2018-03-01

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

F4 symmetric ϕ3 theory at four loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2017-03-01

The renormalization group functions for six dimensional scalar ϕ3 theory with an F4 symmetry are provided at four loops in the modified minimal subtraction (MS ¯ ) scheme. Aside from the anomalous dimension of ϕ and the β -function this includes the mass operator and a ϕ2-type operator. The anomalous dimension of the latter is computed explicitly at four loops for the 26 and 324 representations of F4. The ɛ expansion of all the related critical exponents are determined to O (ɛ4). For instance the value for Δϕ agrees with recent conformal bootstrap estimates in 5 and 5.95 dimensions. The renormalization group functions are also provided at four loops for the group E6.

Variational optimization algorithms for uniform matrix product states

NASA Astrophysics Data System (ADS)

Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

2018-01-01

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

Improving the In-Medium Similarity Renormalization Group via approximate inclusion of three-body effects

NASA Astrophysics Data System (ADS)

Morris, Titus; Bogner, Scott

2016-09-01

The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully to the ground state of closed shell finite nuclei. Recent work has extended its ability to target excited states of these closed shell systems via equation of motion methods, and also complete spectra of the whole SD shell via effective shell model interactions. A recent alternative method for solving of the IM-SRG equations, based on the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.

Renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, Leslie M.

1989-01-01

The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling.

Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables

NASA Astrophysics Data System (ADS)

Khellat, M. R.; Mirjalili, A.

2017-03-01

We first consider the idea of renormalization group-induced estimates, in the context of optimization procedures, for the Brodsky-Lepage-Mackenzie approach to generate higher-order contributions to QCD perturbative series. Secondly, we develop the deviation pattern approach (DPA) in which through a series of comparisons between lowerorder RG-induced estimates and the corresponding analytical calculations, one could modify higher-order RG-induced estimates. Finally, using the normal estimation procedure and DPA, we get estimates of αs4 corrections for the Bjorken sum rule of polarized deep-inelastic scattering and for the non-singlet contribution to the Adler function.

Renormalization-Group Theory Study of Superfluidity and Phase Separation of Helium Mixtures Immersed in Jungle-Gym Aerogel

NASA Astrophysics Data System (ADS)

Lopatnikova, Anna; Berker, A. Nihat

1997-03-01

Superfluidity and phase separation in ^3He-^4He mixtures immersed in jungle-gym (non-random) aerogel are studied by renormalization-group theory.(Phys. Rev. B, in press (1996)) Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena, and trends with respect to aerogel concentration, are explained by the connectivity and tenuousness of jungle-gym aerogel.

Renormalization-group study of superfluidity and phase separation of helium mixtures immersed in a nonrandom aerogel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lopatnikova, A.; Berker, A.N.

1997-02-01

Superfluidity and phase separation in {sup 3}He-{sup 4}He mixtures immersed in a jungle-gym (nonrandom) aerogel are studied by renormalization-group theory. Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low {sup 4}He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena and trends with respect to aerogel concentration are explained by the connectivity and tenuousness of a jungle-gym aerogel. {copyright} {ital 1997} {ital The American Physical Society}

Experience with turbulence interaction and turbulence-chemistry models at Fluent Inc.

NASA Technical Reports Server (NTRS)

Choudhury, D.; Kim, S. E.; Tselepidakis, D. P.; Missaghi, M.

1995-01-01

This viewgraph presentation discusses (1) turbulence modeling: challenges in turbulence modeling, desirable attributes of turbulence models, turbulence models in FLUENT, and examples using FLUENT; and (2) combustion modeling: turbulence-chemistry interaction and FLUENT equilibrium model. As of now, three turbulence models are provided: the conventional k-epsilon model, the renormalization group model, and the Reynolds-stress model. The renormalization group k-epsilon model has broadened the range of applicability of two-equation turbulence models. The Reynolds-stress model has proved useful for strongly anisotropic flows such as those encountered in cyclones, swirlers, and combustors. Issues remain, such as near-wall closure, with all classes of models.

Renormalization-group study of the Nagel-Schreckenberg model

NASA Astrophysics Data System (ADS)

Teoh, Han Kheng; Yong, Ee Hou

2018-03-01

We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p =0 , the dynamics remain invariant in each renormalization-group (RG) transformation. Two fully attractive fixed points, ρc*=0 and 1, and one unstable fixed point, ρc*=1 /(vmax+1 ) , are obtained. The critical exponent ν which is related to the correlation length is calculated for various vmax. The critical exponent appears to decrease weakly with vmax from ν =1.62 to the asymptotical value of 1.00. For the random case p >0 , the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p →0 is studied with simulation, and the RG flow in the ρ -p plane is obtained. The fixed points p =0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.

2017-12-01

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Line Interference Effects Using a Refined Robert-Bonamy Formalism: the Test Case of the Isotropic Raman Spectra of Autoperturbed N2

NASA Technical Reports Server (NTRS)

Boulet, Christian; Ma, Qiancheng; Thibault, Franck

2014-01-01

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

Evanescent effects can alter ultraviolet divergences in quantum gravity without physical consequences

DOE PAGES

Bern, Zvi; Cheung, Clifford; Chi, Huan -Hang; ...

2015-11-17

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D = 4 dimensions. Similarly, evanescent fields do not propagate in D = 4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R 3 counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual inmore » D = 4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly—the coefficient of the Gauss-Bonnet operator—changes under p-form duality transformations. In addition, we concur and also find that the leading R 3 divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.« less

Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences.

PubMed

Bern, Zvi; Cheung, Clifford; Chi, Huan-Hang; Davies, Scott; Dixon, Lance; Nohle, Josh

2015-11-20

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R^{3} counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D=4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly-the coefficient of the Gauss-Bonnet operator-changes under p-form duality transformations. We concur and also find that the leading R^{3} divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.

E-cigarette Marketing and Older Smokers: Road to Renormalization

PubMed Central

Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

2015-01-01

Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681

Two-loop hard-thermal-loop thermodynamics with quarks

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Petitgirard, Emmanuel; Strickland, Michael

2004-08-01

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for Nf=2 and with exact numerical results obtained in the large-Nf limit.

Precise MS light-quark masses from lattice QCD in the regularization invariant symmetric momentum-subtraction scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbahn, Martin; Jaeger, Sebastian; Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH

2010-12-01

We compute the conversion factors needed to obtain the MS and renormalization-group-invariant (RGI) up, down, and strange quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM{sub {gamma}{sub {mu}} }renormalization schemes. This is important for obtaining the MS masses with the best possible precision from numerical lattice QCD simulations, because the customary RI{sup (')}/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scalemore » dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM{sub {gamma}{sub {mu}} }scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.« less

Nontrivial thermodynamics in 't Hooft's large-N limit

NASA Astrophysics Data System (ADS)

Cubero, Axel Cortés

2015-05-01

We study the finite volume/temperature correlation functions of the (1 +1 )-dimensional SU (N ) principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large N , and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

Chiral algebras in Landau-Ginzburg models

NASA Astrophysics Data System (ADS)

Dedushenko, Mykola

2018-03-01

Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.

Fine structure of the entanglement entropy in the O(2) model.

PubMed

Yang, Li-Ping; Liu, Yuzhi; Zou, Haiyuan; Xie, Z Y; Meurice, Y

2016-01-01

We compare two calculations of the particle density in the superfluid phase of the O(2) model with a chemical potential μ in 1+1 dimensions. The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG) formulation of the transfer matrix. The second is a worm algorithm. We show that the particle number distributions obtained with the two methods agree well. We use the TRG method to calculate the thermal entropy and the entanglement entropy. We describe the particle density, the two entropies and the topology of the world lines as we increase μ to go across the superfluid phase between the first two Mott insulating phases. For a sufficiently large temporal size, this process reveals an interesting fine structure: the average particle number and the winding number of most of the world lines in the Euclidean time direction increase by one unit at a time. At each step, the thermal entropy develops a peak and the entanglement entropy increases until we reach half-filling and then decreases in a way that approximately mirrors the ascent. This suggests an approximate fermionic picture.

Entangled quantum electronic wavefunctions of the Mn₄CaO₅ cluster in photosystem II.

PubMed

Kurashige, Yuki; Chan, Garnet Kin-Lic; Yanai, Takeshi

2013-08-01

It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 10(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.

Quantum Ultra-Walks: Walks on a Line with Spatial Disorder

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Falkner, Stefan

We discuss the model of a heterogeneous discrete-time walk on a line with spatial disorder in the form of a set of ultrametric barriers. Simulations show that such an quantum ultra-walk spreads with a walk exponent dw that ranges from ballistic (dw = 1) to complete confinement (dw = ∞) for increasing separation 1 <= 1 / ɛ < ∞ in barrier heights. We develop a formalism by which the classical random walk as well as the quantum walk can be treated in parallel using a coined walk with internal degrees of freedom. For the random walk, this amounts to a 2nd -order Markov process with a stochastic coin, better know as an (anti-)persistent walk. The exact analysis, based on the real-space renormalization group (RG), reproduces the results of the well-known model of ``ultradiffusion,'' dw = 1 -log2 ɛ for 0 < ɛ <= 1 / 2 . However, while the evaluation of the RG fixed-points proceeds virtually identical, for the corresponding quantum walk with a unitary coin it fails to reproduce the numerical results. A new way to analyze the RG is indicated. Supported by NSF-DMR 1207431.

Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories

DOE PAGES

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

2016-10-17

We establish a linear relation between the a-type Weyl anomaly and the ’t Hooft anomaly coeffcients for the R-symmetry and gravitational anomalies in sixdimensional (1,0) superconformal field theories. For RG flows onto the tensor branch, where conformal symmetry is spontaneously broken, supersymmetry relates the anomaly mismatch Δa to the square of a four-derivative interaction for the dilaton. This establishes the a-theorem for all such flows. The four-derivative dilaton interaction is in turn related to the Green-Schwarz-like terms that are needed to match the ’t Hooft anomalies on the tensor branch, thus fixing their relation to Δa. We use our formulamore » to obtain exact expressions for the a-anomaly of N small E 8 instantons, as well as N M 5-branes probing an orbifold singularity, and verify the a-theorem for RG flows onto their Higgs branches. We also discuss aspects of supersymmetric RG flows that terminate in scale but not conformally invariant theories with massless gauge fields.« less

Role of the pair potential for the saturation of generalized Pauli constraints

NASA Astrophysics Data System (ADS)

Legeza, Örs; Schilling, Christian

2018-05-01

The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically confined and interact by pair potentials of the form | xi-xj|s with -1 ≤s ≤5 . We use the density matrix renormalization group approach and large orbital basis to achieve the convergence on more than ten digits of both the variational energy and the natural occupation numbers. Our results confirm that the conflict between energy minimization and fermionic exchange symmetry results in a universal and nontrivial quasisaturation of the generalized Pauli constraints (quasipinning), implying tremendous structural simplifications of the fermionic ground state for all s . Those numerically exact results are complemented by an analytical study based on a self-consistent perturbation theory which we develop for this purpose. The respective results for the weak-coupling regime eventually elucidate the singular behavior found for the specific values s =2 ,4 ,..., resulting in an extremely strong quasipinning.

Exploring the nonequilibrium dynamics of ultracold quantum gases by using numerical tools

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian

Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al., in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis, nonequilibrium mass transport, dynamical fermionization, and transient phenomena such as quantum distillation or dynamical quasicondensation. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems and in determining the asymptotic state after a quantum quench. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 801.

Fermion-induced quantum critical points in two-dimensional Dirac semimetals

NASA Astrophysics Data System (ADS)

Jian, Shao-Kai; Yao, Hong

2017-11-01

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and Z3-ordered phases (e.g., Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first order. From large-N renormalization-group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nat. Commun. 8, 314 (2017), 10.1038/s41467-017-00167-6] occur when N (the number of flavors of four-component Dirac fermions) is larger than a critical value Nc. Remarkably, from the knowledge of space-time supersymmetry, we obtain an exact lower bound for Nc, i.e., Nc>1 /2 . (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., ν ≠ν' , by large-N RG calculations. We further give a brief discussion of possible experimental realizations of FIQCPs.

Baby de Sitter black holes and dS3/CFT2

NASA Astrophysics Data System (ADS)

de Buyl, Sophie; Detournay, Stéphane; Giribet, Gaston; Ng, Gim Seng

2014-02-01

Unlike three-dimensional Einstein gravity, three-dimensional massive gravity admits asymptotically de Sitter space (dS) black hole solutions. These black holes present interesting features and provide us with toy models to study the dS/CFT correspondence. A remarkable property of these black holes is that they are always in thermal equilibrium with the cosmological horizon of the space that hosts them. This invites us to study the thermodynamics of these solutions within the context of dS/CFT. We study the asymptotic symmetry group of the theory and find that it indeed coincides with the local two-dimensional conformal algebra. The charge algebra associated to the asymptotic Killing vectors consists of two copies of the Virasoro algebra with non-vanishing central extension. We compute the mass and angular momentum of the dS black holes and verify that a naive application of Cardy's formula exactly reproduces the entropy of both the black hole and the cosmological horizon. By adapting the holographic renormalization techniques to the case of dS space, we define the boundary stress tensor of the dual Euclidean conformal field theory.

Renormalization shielding effect on the Wannier-ridge mode for double-electron continua in partially ionized dense hydrogen plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590

2016-01-15

The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wanniermore » exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.« less

Functional renormalization group approach to the Yang-Lee edge singularity

DOE PAGES

An, X.; Mesterházy, D.; Stephanov, M. A.

2016-07-08

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Functional renormalization group approach to the Yang-Lee edge singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, X.; Mesterházy, D.; Stephanov, M. A.

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Finite-size scaling study of the two-dimensional Blume-Capel model

NASA Astrophysics Data System (ADS)

Beale, Paul D.

1986-02-01

The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (Tt=0.610+/-0.005, Dt=1.9655+/-0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.

Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.

PubMed

Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano

2007-10-05

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.

Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics

NASA Astrophysics Data System (ADS)

Baldovin, F.; Robledo, A.

2002-10-01

We uncover the dynamics at the chaos threshold μ∞ of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for μ<μ∞. We corroborate this structure analytically via the Feigenbaum renormalization-group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential, of which we determine the q index and the q-generalized Lyapunov coefficient λq. Our results are an unequivocal validation of the applicability of the nonextensive generalization of Boltzmann-Gibbs statistical mechanics to critical points of nonlinear maps.

Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near (1)/(4) doping

NASA Astrophysics Data System (ADS)

Wang, Wan-Sheng; Xiang, Yuan-Yuan; Wang, Qiang-Hua; Wang, Fa; Yang, Fan; Lee, Dung-Hai

2012-01-01

We study the electronic instabilities of near 1/4 electron doped graphene using the singular-mode functional renormalization group, with a self-adaptive k mesh to improve the treatment of the van Hove singularities, and variational Monte Carlo method. At 1/4 doping the system is a chiral spin-density wave state exhibiting the anomalous quantized Hall effect. When the doping deviates from 1/4, the dx2-y2+idxy Cooper pairing becomes the leading instability. Our results suggest that near 1/4 electron or hole doping (away from the neutral point) the graphene is either a Chern insulator or a topoligical superconductor.

Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion

NASA Astrophysics Data System (ADS)

Moon, Sung Pil

2018-06-01

We examine a suggested relation between stochastic quantization and the holographic Wilsonian renormalization group in the massive fermion case on Euclidean AdS space. The original suggestion about the general relation between the two theories is posted in arXiv:1209.2242. In the previous researches, it is already verified that scalar fields, U(1) gauge fields, and massless fermions are consistent with the relation. In this paper, we examine the relation in the massive fermion case. Contrary to the other case, in the massive fermion case, the action needs particular boundary terms to satisfy boundary conditions. We finally confirm that the proposed suggestion is also valid in the massive fermion case.

On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

NASA Technical Reports Server (NTRS)

Smith, L. M.; Reynolds, W. C.

1992-01-01

An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

Development of renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, L. M.

1990-01-01

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays

NASA Technical Reports Server (NTRS)

Chiu, H. H.

1989-01-01

The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.

Quantum multicriticality in disordered Weyl semimetals

NASA Astrophysics Data System (ADS)

Luo, Xunlong; Xu, Baolong; Ohtsuki, Tomi; Shindou, Ryuichi

2018-01-01

In electronic band structure of solid-state material, two band-touching points with linear dispersion appear in pairs in the momentum space. When they annihilate each other, the system undergoes a quantum phase transition from a three-dimensional (3D) Weyl semimetal (WSM) phase to a band insulator phase such as a Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a "magnetic dipole"-like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases: a renormalized WSM phase, a CI phase, and a diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band-touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states, and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized WSM phase turns out to be a direct phase transition whose critical exponent ν =0.80 ±0.01 . We interpret these numerical results by a renormalization group analysis on the critical theory.

Holographic renormalization group and cosmology in theories with quasilocalized gravity

NASA Astrophysics Data System (ADS)

Csáki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John

2001-03-01

We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.

Holographic renormalization group and cosmology in theories with quasilocalized gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.

2001-03-15

We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowskimore » space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.« less

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models.

PubMed

Antonov, N V; Gulitskiy, N M; Kostenko, M M; Malyshev, A V

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E∝k^{1-y} and the dispersion law ω∝k^{2-η}. The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

NASA Astrophysics Data System (ADS)

Rodrigues, Davi C.; Mauro, Sebastião; de Almeida, Álefe O. F.

2016-10-01

General relativity extensions based on renormalization group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post-Newtonian limits of a realization called renormalization group extended general relativity (RGGR). Special attention is given to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter ν¯⊙, and this parameter is such that for ν¯⊙=0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν¯ ⊙|≲10-21 , without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the parametrized post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on ν¯⊙, either considering or not the external potential effect. With the external potential effect the new bound reads |ν¯ ⊙|≲10-16 . We discuss the possible consequences of this bound on the dark matter abundance in galaxies.

Renormalization group flows and continual Lie algebras

NASA Astrophysics Data System (ADS)

Bakas, Ioannis

2003-08-01

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

Horizon as critical phenomenon

NASA Astrophysics Data System (ADS)

Lee, Sung-Sik

2016-09-01

We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U( N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions

NASA Astrophysics Data System (ADS)

Lee, Yu-Wen; Lee, Yu-Li

2018-01-01

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994), 10.1103/RevModPhys.66.129], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

Weyl consistency conditions in non-relativistic quantum field theory

DOE PAGES

Pal, Sridip; Grinstein, Benjamín

2016-12-05

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2 + 1 dimensions with anisotropic scaling exponent z = 2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. Here, we comment on possible candidates for a C-theorem in higher dimensions.

Quantization of the nonlinear sigma model revisited

NASA Astrophysics Data System (ADS)

Nguyen, Timothy

2016-08-01

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

NASA Astrophysics Data System (ADS)

Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.

2017-07-01

We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions d →2 . Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, 2 αF=2 -d and 2 αG=d at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.

Power counting and Wilsonian renormalization in nuclear effective field theory

NASA Astrophysics Data System (ADS)

Valderrama, Manuel Pavón

2016-05-01

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

A shape dynamical approach to holographic renormalization

NASA Astrophysics Data System (ADS)

Gomes, Henrique; Gryb, Sean; Koslowski, Tim; Mercati, Flavio; Smolin, Lee

2015-01-01

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities.

Fourier transform for fermionic systems and the spectral tensor network.

PubMed

Ferris, Andrew J

2014-07-04

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

PubMed Central

Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

2016-01-01

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials. PMID:27578363

Mass deformations of 5d SCFTs via holography

NASA Astrophysics Data System (ADS)

Gutperle, Michael; Kaidi, Justin; Raj, Himanshu

2018-02-01

Using six-dimensional Euclidean F (4) gauged supergravity we construct a holographic renormalization group flow for a CFT on S 5. Numerical solutions to the BPS equations are obtained and the free energy of the theory on S 5 is determined holographically by calculation of the renormalized on-shell supergravity action. In the process, we deal with subtle issues such as holographic renormalization and addition of finite counterterms. We then propose a candidate field theory dual to these solutions. This tentative dual is a supersymmetry-preserving deformation of the strongly-coupled non-Lagrangian SCFT derived from the D4-D8 system in string theory. In the IR, this theory is a mass deformation of a USp(2 N ) gauge theory. A localization calculation of the free energy is performed for this IR theory, which for reasonably small values of the deformation parameter is found to have the same qualitative behaviour as the holographic free energy.

Baryon chiral perturbation theory extended beyond the low-energy region.

PubMed

Epelbaum, E; Gegelia, J; Meißner, Ulf-G; Yao, De-Liang

We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.

Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

PubMed

Jurčišinová, E; Jurčišin, M

2017-05-01

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Canonical Drude Weight for Non-integrable Quantum Spin Chains

NASA Astrophysics Data System (ADS)

Mastropietro, Vieri; Porta, Marcello

2018-03-01

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.

Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the 'Standard Values'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pogorelov, A. A.; Suslov, I. M.

2008-06-15

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called standard values), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors of the standardmore » values and for a further increase in accuracy.« less

Renormalization Group Theory, the Epsilon Expansion and Ken Wilson as I knew Him

NASA Astrophysics Data System (ADS)

Fisher, Michael E.

The tasks posed for renormalization group theory (RGT) within statistical physics by critical phenomena theory in the 1960's are set out briefly in contradistinction to quantum field theory (QFT), which was the origin for Ken Wilson's concerns. Kadanoff's 1966 block spin scaling picture and its difficulties are presented;Wilson's early vision of flows is described from the author's perspective. How Wilson's subsequent breakthrough ideas, published in 1971, led to the epsilon expansion and the resulting clarity is related. Concluding sections complete the general picture of flows in a space of Hamiltonians, universality and scaling. The article represents a 40% condensation (but with added items) of an earlier account: Rev. Mod. Phys. 70, 653-681 (1998).

Renormalization Group Tutorial

NASA Technical Reports Server (NTRS)

Bell, Thomas L.

2004-01-01

Complex physical systems sometimes have statistical behavior characterized by power- law dependence on the parameters of the system and spatial variability with no particular characteristic scale as the parameters approach critical values. The renormalization group (RG) approach was developed in the fields of statistical mechanics and quantum field theory to derive quantitative predictions of such behavior in cases where conventional methods of analysis fail. Techniques based on these ideas have since been extended to treat problems in many different fields, and in particular, the behavior of turbulent fluids. This lecture will describe a relatively simple but nontrivial example of the RG approach applied to the diffusion of photons out of a stellar medium when the photons have wavelengths near that of an emission line of atoms in the medium.

Non-local geometry inside Lifshitz horizon

NASA Astrophysics Data System (ADS)

Hu, Qi; Lee, Sung-Sik

2017-07-01

Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.

The renormalization scale-setting problem in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scalemore » ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending BLM up to any perturbative order; in fact, they are equivalent to each other through the PMC–BLM correspondence principle. Thus, all the features previously observed in the BLM literature are also adaptable to the PMC. The PMC scales and the resulting finite-order PMC predictions are to high accuracy independent of the choice of the initial renormalization scale, and thus consistent with RG invariance. The PMC is also consistent with the renormalization scale-setting procedure for QED in the zero-color limit. The use of the PMC thus eliminates a serious systematic scale error in perturbative QCD predictions, greatly improving the precision of empirical tests of the Standard Model and their sensitivity to new physics.« less

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boulet, Christian, E-mail: Christian.boulet@u-psud.fr; Ma, Qiancheng; Thibault, Franck

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N{sub 2} for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While inmore » the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N{sub 2}, opening the way to the analysis of more complex molecular systems.« less

Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids—The renormalized ALDA and electron gas kernels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patrick, Christopher E., E-mail: chripa@fysik.dtu.dk; Thygesen, Kristian S., E-mail: thygesen@fysik.dtu.dk

2015-09-14

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence, or (c) display a 1/k{sup 2} divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a testmore » set of 10 solids consisting of tetrahedrally bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF), and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H{sub 2} molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA’s tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.« less

Testing the renormalisation group theory of cooperative transitions at the lambda point of helium

NASA Technical Reports Server (NTRS)

Lipa, J. A.; Li, Q.; Chui, T. C. P.; Marek, D.

1988-01-01

The status of high resolution tests of the renormalization group theory of cooperative phase transitions performed near the lambda point of helium is described. The prospects for performing improved tests in space are discussed.

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Random sequential renormalization and agglomerative percolation in networks: application to Erdös-Rényi and scale-free graphs.

PubMed

Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

2011-12-01

We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song et al., Nature (London) 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N(0) → 0 in the limit of large systems (where N(0) is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N(0) in sparse ER graphs and in the annealed model, while it happens for N/N(0) → 1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi et al. [Phys. Rev. Lett. 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering "supernodes" as clusters) are much easier to study using the fast Newman-Ziff algorithm for percolation, allowing us to obtain very high statistics.

Finite-size scaling and integer-spin Heisenberg chains

NASA Astrophysics Data System (ADS)

Bonner, Jill C.; Müller, Gerhard

1984-03-01

Finite-size scaling (phenomenological renormalization) techniques are trusted and widely applied in low-dimensional magnetism and, particularly, in lattice gauge field theory. Recently, investigations have begun which subject the theoretical basis to systematic and intensive scrutiny to determine the validity of finite-size scaling in a variety of situations. The 2D ANNNI model is an example of a situation where finite-size scaling methods encounter difficulty, related to the occurrence of a disorder line (one-dimensional line). A second example concerns the behavior of the spin-1/2 antiferromagnetic XXZ model where the T=0 critical behavior is exactly known and features an essential singularity at the isotropic Heisenberg point. Standard finite-size scaling techniques do not convincingly reproduce the exact phase behavior and this is attributable to the essential singularity. The point is relevant in connection with a finite-size scaling analysis of a spin-one antiferromagnetic XXZ model, which claims to support a conjecture by Haldane that the T=0 phase behavior of integer-spin Heisenberg chains is significantly different from that of half-integer-spin Heisenberg chains.

Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group

NASA Astrophysics Data System (ADS)

Dutta, Ayan; Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.

2018-04-01

While the plausibility of formation of limit cycle has been a well studied topic in context of the Poincare-Bendixson theorem, studies on estimates in regard to the possible size and shape of the limit cycle seem to be scanty in the literature. In this paper we present a pedagogical study of some aspects of the size of this limit cycle using perturbative renormalization group by doing detailed and explicit calculations upto second order for the Selkov model for glycolytic oscillations. This famous model is well known to lead to a limit cycle for certain ranges of values of the parameters involved in the problem. Within the tenets of the approximations made, reasonable agreement with the numerical plots can be achieved.

Dissipative exciton transfer in donor-bridge-acceptor systems: numerical renormalization group calculation of equilibrium properties.

PubMed

Tornow, Sabine; Tong, Ning-Hua; Bulla, Ralf

2006-07-05

We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.

Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations

NASA Astrophysics Data System (ADS)

O'Malley, Robert E., Jr.; Williams, David B.

2006-06-01

Results by physicists on renormalization group techniques have recently sparked interest in the singular perturbations community of applied mathematicians. The survey paper, [Phys. Rev. E 54(1) (1996) 376-394], by Chen et al. demonstrated that many problems which applied mathematicians solve using disparate methods can be solved using a single approach. Analysis of that renormalization group method by Mudavanhu and O'Malley [Stud. Appl. Math. 107(1) (2001) 63-79; SIAM J. Appl. Math. 63(2) (2002) 373-397], among others, indicates that the technique can be streamlined. This paper carries that analysis several steps further to present an amplitude equation technique which is both well adapted for use with a computer algebra system and easy to relate to the classical methods of averaging and multiple scales.

Symmetry-conserving purification of quantum states within the density matrix renormalization group

DOE PAGES

Nocera, Alberto; Alvarez, Gonzalo

2016-01-28

The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less

Hybrid Defect Phase Transition: Renormalization Group and Monte Carlo Analysis

NASA Astrophysics Data System (ADS)

Kaufman, Miron; Diep, H. T.

2010-03-01

For the q-state Potts model with 2 < q <= 4 on the square lattice with a defect line, the order parameter on the defect line jumps discontinuously from zero to a nonzero value while the defect energy varies continuously with the temperature at the critical temperature. Monte-Carlo simulations (H. T. Diep, M. Kaufman, Phys Rev E 2009) of the q-state Potts model on a square lattice with a line of defects verify the renormalization group prediction (M. Kaufman, R. B. Griffiths, Phys Rev B 1982) on the occurrence of the hybrid transition on the defect line. This is interesting since for those q values the bulk transition is continuous. This hybrid (continuous - discontinuous) defect transition is induced by the infinite range correlations at the bulk critical point.

Multiloop functional renormalization group for general models

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018), 10.1103/PhysRevLett.120.057403] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.

Supersymmetric QCD on the lattice: An exploratory study

NASA Astrophysics Data System (ADS)

Costa, M.; Panagopoulos, H.

2017-08-01

We perform a pilot study of the perturbative renormalization of a supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider supersymmetric N =1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naïve discretization. The gauge group that we consider is S U (Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α , are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (Zψ), gluon (Zu), gluino (Zλ), squark (ZA ±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

The Conformal Template and New Perspectives for Quantum Chromodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brodsky, Stanley J.; /SLAC

2007-03-06

Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically tractable approximation to QCD in the regime where the QCD coupling is large and constant. For example, there is an exact correspondence between the fifth-dimensional coordinate of AdS space and a specific impact variable which measures the separation of the quark constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, themore » fundamental entities which encode hadron properties and allow the computation of exclusive scattering amplitudes. One can also use conformal symmetry as a template for perturbative QCD predictions where the effects of the nonzero beta function can be systematically included in the scale of the QCD coupling. This leads to fixing of the renormalization scale and commensurate scale relations which relate observables without scale or scheme ambiguity. The results are consistent with the renormalization group and the analytic connection of QCD to Abelian theory at N{sub C} {yields} 0. I also discuss a number of novel phenomenological features of QCD. Initial- and .nal-state interactions from gluon-exchange, normally neglected in the parton model, have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, di.ractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss tests of hidden color in nuclear wavefunctions, the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, nonperturbative antisymmetric sea quark distributions, anomalous heavy quark e.ects, and the unexpected effects of direct higher-twist processes.« less

Flux Renormalization in Constant Power Burnup Calculations

DOE PAGES

Isotalo, Aarno E.; Aalto Univ., Otaniemi; Davidson, Gregory G.; ...

2016-06-15

To more accurately represent the desired power in a constant power burnup calculation, the depletion steps of the calculation can be divided into substeps and the neutron flux renormalized on each substep to match the desired power. Here, this paper explores how such renormalization should be performed, how large a difference it makes, and whether using renormalization affects results regarding the relative performance of different neutronics–depletion coupling schemes. When used with older coupling schemes, renormalization can provide a considerable improvement in overall accuracy. With previously published higher order coupling schemes, which are more accurate to begin with, renormalization has amore » much smaller effect. Finally, while renormalization narrows the differences in the accuracies of different coupling schemes, their order of accuracy is not affected.« less

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

NASA Astrophysics Data System (ADS)

Yadav, Ravi; Bogdanov, Nikolay A.; Katukuri, Vamshi M.; Nishimoto, Satoshi; van den Brink, Jeroen; Hozoi, Liviu

2016-11-01

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3.

PubMed

Yadav, Ravi; Bogdanov, Nikolay A; Katukuri, Vamshi M; Nishimoto, Satoshi; van den Brink, Jeroen; Hozoi, Liviu

2016-11-30

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d 5 honeycomb halide α-RuCl 3 . From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general.

Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb.

PubMed

Agrapidis, Cliò Efthimia; van den Brink, Jeroen; Nishimoto, Satoshi

2018-01-29

We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points [Formula: see text] and [Formula: see text] are singular. The ϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl 3 , a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

PubMed Central

Yadav, Ravi; Bogdanov, Nikolay A.; Katukuri, Vamshi M.; Nishimoto, Satoshi; van den Brink, Jeroen; Hozoi, Liviu

2016-01-01

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general. PMID:27901091

Quantum spin chains with multiple dynamics

NASA Astrophysics Data System (ADS)

Chen, Xiao; Fradkin, Eduardo; Witczak-Krempa, William

2017-11-01

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤z <2.7 , which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.

Long-range Coulomb interaction effects on the topological phase transitions between semimetals and insulators

NASA Astrophysics Data System (ADS)

Han, SangEun; Moon, Eun-Gook

2018-06-01

Topological states may be protected by a lattice symmetry in a class of topological semimetals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space concretely defines a chirality, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include a Dirac semimetal (DSM) in a distorted spinel, BiZnSiO4, protected by a mirror symmetry, and a DSM in Na3Bi , protected by a rotational symmetry. In these states, topology and chiral symmetry are intrinsically tied. In this Rapid Communication, the characteristic interplay between a chiral symmetry order parameter and an instantaneous long-range Coulomb interaction is investigated with the standard renormalization group method. We show that a topological transition associated with chiral symmetry is stable under the presence of a Coulomb interaction and the electron velocity always becomes faster than the one of a chiral symmetry order parameter. Thus, the transition must not be relativistic, which implies that supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. Asymptotically exact universal ratios of physical quantities such as the energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

Particle-hole symmetry, many-body localization, and topological edge modes

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).

Drell-Yan production at small q T , transverse parton distributions and the collinear anomaly

NASA Astrophysics Data System (ADS)

Becher, Thomas; Neubert, Matthias

2011-06-01

Using methods from effective field theory, an exact all-order expression for the Drell-Yan cross section at small transverse momentum is derived directly in q T space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins-Soper-Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A (3) is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of x T -dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and xT2, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small x T onto standard parton distributions is calculated at O(αs), while their anomalous dimensions are known to three loops.

Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity

NASA Astrophysics Data System (ADS)

Mandula, Jeffrey E.; Ogilvie, Michael C.

1997-02-01

We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

Competing orders in the Hofstadter t -J model

NASA Astrophysics Data System (ADS)

Tu, Wei-Lin; Schindler, Frank; Neupert, Titus; Poilblanc, Didier

2018-01-01

The Hofstadter model describes noninteracting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model, including a Hubbard repulsion U . We investigate this model in the large-U limit corresponding to a t -J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean-field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly coexisting) charge, bond, and superconducting orders. Topological properties of the states are also investigated, and some of our results are compared to related experiments involving ultracold atoms loaded on optical lattices in the presence of a synthetic gauge field.

Vacuum polarization of the electromagnetic field near a rotating black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, V.P.; Zel'nikov, A.I.

1985-12-15

The electromagnetic field contribution to the vacuum polarization near a rotating black hole is considered. It is shown that the problem of calculating the renormalized average value of the stress-energy tensor /sup ren/ for the Hartle-Hawking vacuum state at the pole of the event horizon can be reduced to the problem of electro- and magnetostatics in the Kerr spacetime. An explicit expression for /sup ren/ at the pole of the event horizon is obtained and its properties are discussed. It is shown that in the case of a nonrotating black hole the Page-Brown approximation for the electromagnetic stress-energy tensor givesmore » a result which coincides at the event horizon with the exact value of /sup ren/. .AE« less

Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions.

PubMed

Rançon, A; Kodio, O; Dupuis, N; Lecheminant, P

2013-07-01

We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T(3)/c(2))F(N)(Δ/T), where c is the velocity of the excitations at the QCP and |Δ| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F(N). For small values of N (N/~1) regimes, but fails to describe the nonmonotonic behavior of F(N) in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio T(BKT)/ρ(s)(0) is very close to π/2, implying that the stiffness ρ(s)(T(BKT)(-)) at the transition is only slightly reduced with respect to the zero-temperature stiffness ρ(s)(0). Finally, we briefly discuss the experimental determination of the universal function F(2) from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition.

Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach

NASA Astrophysics Data System (ADS)

Grusdt, Fabian; Seetharam, Kushal; Shchadilova, Yulia; Demler, Eugene

2018-03-01

When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fröhlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fröhlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fröhlich model.

Influence of renormalization shielding on the electron-impact ionization process in dense partially ionized plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Mi-Young; Yoon, Jung-Sik; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr

2015-04-15

The renormalization shielding effects on the electron-impact ionization of hydrogen atom are investigated in dense partially ionized plasmas. The effective projectile-target interaction Hamiltonian and the semiclassical trajectory method are employed to obtain the transition amplitude as well as the ionization probability as functions of the impact parameter, the collision energy, and the renormalization parameter. It is found that the renormalization shielding effect suppresses the transition amplitude for the electron-impact ionization process in dense partially ionized plasmas. It is also found that the renormalization effect suppresses the differential ionization cross section in the peak impact parameter region. In addition, it ismore » found that the influence of renormalization shielding on the ionization cross section decreases with an increase of the relative collision energy. The variations of the renormalization shielding effects on the electron-impact ionization cross section are also discussed.« less

Structure of p-shell nuclei using three-nucleon interactions evolved with the similarity renormalization group

DOE PAGES

Jurgenson, E. D.; Maris, P.; Furnstahl, R. J.; ...

2013-05-13

The similarity renormalization group (SRG) is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. The substantial contribution of both initial and SRG-induced three-nucleon forces requires their consistent evolution in a three-particle basis space before applying them to larger nuclei. While, in principle, the evolved Hamiltonians are unitarily equivalent, in practice the need for basis truncation introduces deviations, which must be monitored. Here we present benchmark no-core full configuration calculations with SRG-evolved interactions in p-shell nuclei over a wide range of softening. As a result, these calculations are used to assessmore » convergence properties, extrapolation techniques, and the dependence of energies, including four-body contributions, on the SRG resolution scale.« less

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elizalde, Emilio; Odintsov, Sergei D.; Pozdeeva, Ekaterina O.

2016-02-01

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflationmore » scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.« less

In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

NASA Astrophysics Data System (ADS)

Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei

We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.

Fermi-edge singularity and the functional renormalization group

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-05-01

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

Renormalization group analysis of anisotropic diffusion in turbulent shear flows

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Barton, J. Michael

1991-01-01

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.

Renormalization group analysis of the Reynolds stress transport equation

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Barton, J. M.

1992-01-01

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

Stability of Dirac Liquids with Strong Coulomb Interaction.

PubMed

Tupitsyn, Igor S; Prokof'ev, Nikolay V

2017-01-13

We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln(L)∼40), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T=0 state with divergent Fermi velocity.

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; de Albuquerque, Douglas F.

1997-02-01

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

Renormalization Group for nonlinear oscillators in the absence of linear restoring force

NASA Astrophysics Data System (ADS)

Sarkar, A.; Bhattacharjee, J. K.

2010-09-01

Perturbative Renormalization Group (RG) has been very useful in probing periodic orbits in two-dimensional dynamical systems (Sarkar A., Bhattacharjee J. K., Chakraborty S. and Banerjee D., arXiv:1005.2858v1 (2010)). The method relies on finding a linear center, around which perturbation analysis is done. However it is not obvious as to how systems devoid of any linear terms may be approached using this method. We propose here how RG can be done even in the absence of linear terms. We successfully apply the method to extract correct results for a variant of the second-order Riccati equation. In this variant the periodic orbit disappears as a parameter is varied. Our RG captures this disappearance correctly. We have also applied the technique successfully on the force-free Van der Pol-Duffing oscillator.

Renormalization group methods for the Reynolds stress transport equations

NASA Technical Reports Server (NTRS)

Rubinstein, R.

1992-01-01

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.

2017-03-01

We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field-theoretic renormalization group. In this approach, scaling properties are related to the fixed points of the renormalization group equations. Previous analysis of this model near the real-world space dimension 3 identified a scaling regime [N. V. Antonov et al., Theor. Math. Phys. 110, 305 (1997), 10.1007/BF02630456]. The aim of the present paper is to explore the existence of additional regimes, which could not be found using the direct perturbative approach of the previous work, and to analyze the crossover between different regimes. It seems possible to determine them near the special value of space dimension 4 in the framework of double y and ɛ expansion, where y is the exponent associated with the random force and ɛ =4 -d is the deviation from the space dimension 4. Our calculations show that there exists an additional fixed point that governs scaling behavior. Turbulent advection of a passive scalar (density) field by this velocity ensemble is considered as well. We demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. The corresponding anomalous exponents, identified as scaling dimensions of certain composite fields, can be systematically calculated as a series in y and ɛ . All calculations are performed in the leading one-loop approximation.

Focus Article: Oscillatory and long-range monotonic exponential decays of electrostatic interactions in ionic liquids and other electrolytes: The significance of dielectric permittivity and renormalized charges

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2018-05-01

A unified treatment of oscillatory and monotonic exponential decays of interactions in electrolytes is displayed, which highlights the role of dielectric response of the fluid in terms of renormalized (effective) dielectric permittivity and charges. An exact, but physically transparent statistical mechanical formalism is thereby used, which is presented in a systematic, pedagogical manner. Both the oscillatory and monotonic behaviors are given by an equation for the decay length of screened electrostatic interactions that is very similar to the classical expression for the Debye length. The renormalized dielectric permittivities, which have similar roles for electrolytes as the dielectric constant has for pure polar fluids, consist in general of several entities with different physical meanings. They are connected to dielectric response of the fluid on the same length scale as the decay length of the screened interactions. Only in cases where the decay length is very long, these permittivities correspond approximately to a dielectric response in the long-wavelength limit, like the dielectric constant for polar fluids. Experimentally observed long-range exponentially decaying surface forces are analyzed as well as the oscillatory forces observed for short to intermediate surface separations. Both occur in some ionic liquids and in concentrated as well as very dilute electrolyte solutions. The coexisting modes of decay are in general determined by the bulk properties of the fluid and not by the solvation of the surfaces; in the present cases, they are given by the behavior of the screened Coulomb interaction of the bulk fluid. The surface-fluid interactions influence the amplitudes and signs or phases of the different modes of the decay, but not their decay lengths and wavelengths. The similarities between some ionic liquids and very dilute electrolyte solutions as regards both the long-range monotonic and the oscillatory decays are analyzed.

Computation of parton distributions from the quasi-PDF approach at the physical point

NASA Astrophysics Data System (ADS)

Alexandrou, Constantia; Bacchio, Simone; Cichy, Krzysztof; Constantinou, Martha; Hadjiyiannakou, Kyriakos; Jansen, Karl; Koutsou, Giannis; Scapellato, Aurora; Steffens, Fernanda

2018-03-01

We show the first results for parton distribution functions within the proton at the physical pion mass, employing the method of quasi-distributions. In particular, we present the matrix elements for the iso-vector combination of the unpolarized, helicity and transversity quasi-distributions, obtained with Nf = 2 twisted mass cloverimproved fermions and a proton boosted with momentum |p→| = 0.83 GeV. The momentum smearing technique has been applied to improve the overlap with the proton boosted state. Moreover, we present the renormalized helicity matrix elements in the RI' scheme, following the non-perturbative renormalization prescription recently developed by our group.

On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Zhendong; Xiao, Yunlong; Liu, Wenjian, E-mail: liuwjbdf@gmail.com

2014-08-07

The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α{supmore » 2} in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α{sup 2}) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.« less

On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties

NASA Astrophysics Data System (ADS)

Li, Zhendong; Xiao, Yunlong; Liu, Wenjian

2014-08-01

The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α2 in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α ^2) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.

Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

PubMed

Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves

2014-01-01

Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

Emergence of Criticality in the Transportation Passenger Flow: Scaling and Renormalization in the Seoul Bus System

PubMed Central

Goh, Segun; Lee, Keumsook; Choi, MooYoung; Fortin, Jean-Yves

2014-01-01

Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) “block stop” and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221

Effects of renormalizing the chiral SU(2) quark-meson model

NASA Astrophysics Data System (ADS)

Zacchi, Andreas; Schaffner-Bielich, Jürgen

2018-04-01

We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory

NASA Astrophysics Data System (ADS)

Evans, Robert; Stewart, Maria C.; Wilding, Nigel B.

2017-07-01

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν∥, which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory.

PubMed

Evans, Robert; Stewart, Maria C; Wilding, Nigel B

2017-07-28

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν ∥ , which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Renormalized Hamiltonian for a peptide chain: Digitalizing the protein folding problem

NASA Astrophysics Data System (ADS)

Fernández, Ariel; Colubri, Andrés

2000-05-01

A renormalized Hamiltonian for a flexible peptide chain is derived to generate the long-time limit dynamics compatible with a coarsening of torsional conformation space. The renormalization procedure is tailored taking into account the coarse graining imposed by the backbone torsional constraints due to the local steric hindrance and the local backbone-side-group interactions. Thus, the torsional degrees of freedom for each residue are resolved modulo basins of attraction in its so-called Ramachandran map. This Ramachandran renormalization (RR) procedure is implemented so that the chain is energetically driven to form contact patterns as their respective collective topological constraints are fulfilled within the coarse description. In this way, the torsional dynamics are digitalized and become codified as an evolving pattern in a binary matrix. Each accepted Monte Carlo step in a canonical ensemble simulation is correlated with the real mean first passage time it takes to reach the destination coarse topological state. This real-time correlation enables us to test the RR dynamics by comparison with experimentally probed kinetic bottlenecks along the dominant folding pathway. Such intermediates are scarcely populated at any given time, but they determine the kinetic funnel leading to the active structure. This landscape region is reached through kinetically controlled steps needed to overcome the conformational entropy of the random coil. The results are specialized for the bovine pancreatic trypsin inhibitor, corroborating the validity of our method.

Assessing notions of denormalization and renormalization of smoking in light of e-cigarette regulation.

PubMed

Sæbø, Gunnar; Scheffels, Janne

2017-11-01

The rationale for 'denormalization' of smoking in tobacco policies has been challenged by the emergence of e-cigarettes and the need to regulate e-cigarette use and promotion. Our aim is to assess the research status on e-cigarettes' contribution to 'renormalization' of smoking and to clarify how renormalization of smoking can be appraised at the conceptual and empirical level. Combining conceptual analysis and narrative review, the paper brings out three dimensions of denormalization/renormalization of smoking ('unacceptability/acceptability'; 'invisibility/visibility'; 'phasing out behaviour/maintaining behaviour') and an inherent duality of the e-cigarette as a smoking-like device and a smoking alternative. These analytical dimensions are applied qualitatively to consider the literature identified by searching the Web of Science database for 'e-cigarettes AND renormalization' (and variants thereof). Theoretically, normative changes in smoking acceptability, increased visibility of e-cigarettes and use, and observations of actual use (prevalence, dual use, gateway) can all be applied to illustrate processes of renormalization. However, only acceptability measures and user measures can be said to be empirical tests of renormalization effects. Visibility measures are only based on logical assumptions of a possible renormalization; they are not in themselves indicative of any "real" renormalization effects and can just as well be understood as possible consequences of normalization of e-cigarettes. Just as a downward trend in smoking prevalence is the litmus test of whether denormalization policy works, stagnating or rising smoking prevalence should be the main empirical indicator of renormalization. Copyright © 2017 Elsevier B.V. All rights reserved.

Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kniehl, Bernd A.; Sirlin, Alberto

2006-12-01

We present an on-shell scheme to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave function renormalization contributions, and to implement the on-shell renormalization of the former with nondiagonal mass counterterm matrices. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.

Criticality of the random field Ising model in and out of equilibrium: A nonperturbative functional renormalization group description

NASA Astrophysics Data System (ADS)

Balog, Ivan; Tarjus, Gilles; Tissier, Matthieu

2018-03-01

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension dD R≈5.1 . We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dD R, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

Nonlinear relativistic plasma resonance: Renormalization group approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Metelskii, I. I., E-mail: metelski@lebedev.ru; Kovalev, V. F., E-mail: vfkvvfkv@gmail.com; Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy ofmore » the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.« less

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE Office of Scientific and Technical Information (OSTI.GOV)

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE PAGES

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

2017-04-15

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Ground states of linear rotor chains via the density matrix renormalization group

NASA Astrophysics Data System (ADS)

Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

2018-04-01

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

A state interaction spin-orbit coupling density matrix renormalization group method

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2016-06-01

We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe2S2(SCH3)4]3-, determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.

Oscillators: Old and new perspectives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharjee, Jayanta K.; Roy, Jyotirmoy

We consider some of the well known oscillators in literature which are known to exhibit interesting effects of nonlinearity. We review the Lindstedt-Poincare technique for dealing with with the nonlinear effects and then go on to introduce the relevance of the renormalization group for the oscillator following the pioneering work of Chen et al. It is pointed out that the traditional Lindstedt-Poincare and the renormalization group techniques have operational connections. We use this to find an unexpected mode softening in the double pendulum. This mode softening prompted us to look for chaos in the double pendulum at low energies-energies thatmore » are just sufficient to allow the outer pendulum to rotate (the double pendulum is known to be chaotic at high energies-energies that are greater than that needed to make both pendulums to rotate). The emergence of the chaos is strongly dependent on initial conditions.« less

Numerical renormalization group method for entanglement negativity at finite temperature

NASA Astrophysics Data System (ADS)

Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.

2018-04-01

We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots

NASA Astrophysics Data System (ADS)

Khedri, A.; Meden, V.; Costi, T. A.

2017-11-01

We investigate the effect of vibrational degrees of freedom on the linear thermoelectric transport through a single-level quantum dot described by the spinless Anderson-Holstein impurity model. To study the effects of strong electron-phonon coupling, we use the nonperturbative numerical renormalization group approach. We also compare our results, at weak to intermediate coupling, with those obtained by employing the functional renormalization group method, finding good agreement in this parameter regime. When applying a gate voltage at finite temperatures, the inelastic scattering processes, induced by phonon-assisted tunneling, result in an interesting interplay between electrical and thermal transport. We explore different parameter regimes and identify situations for which the thermoelectric power as well as the dimensionless figure of merit are significantly enhanced via a Mahan-Sofo type of mechanism. We show, in particular, that this occurs at strong electron-phonon coupling and in the antiadiabatic regime.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis

NASA Astrophysics Data System (ADS)

Tsuchiizu, Masahisa; Kawaguchi, Kouki; Yamakawa, Youichi; Kontani, Hiroshi

2018-04-01

Recently, complex rotational symmetry-breaking phenomena have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various unconventional charge susceptibilities in an unbiased way by applying the functional-renormalization-group method to the d -p Hubbard model. Without assuming the wave vector of the order parameter, we reveal that the most dominant instability is the uniform (q =0 ) charge modulation on the px and py orbitals, which possesses d symmetry. This uniform nematic order triggers another nematic p -orbital density wave along the axial (Cu-Cu) direction at Qa≈(π /2 ,0 ) . It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at q =Qa is triggered by the uniform order. The predicted multistage nematic transitions are caused by Aslamazov-Larkin-type fluctuation-exchange processes.

Renormalization group theory for percolation in time-varying networks.

PubMed

Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

2018-05-22

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

Tau hadronic spectral function moments: perturbative expansion and αs extractions

NASA Astrophysics Data System (ADS)

Boito, D.

2016-04-01

In the extraction of αs from hadronic τ decays different moments of the spectral functions have been used. Furthermore, the two mainstream renormalization group improvement (RGI) frameworks, namely Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT), lead to conflicting values of αs. In order to improve the strategy used in αs determinations, we have performed a systematic study of the perturbative behaviour of these spectral moments in the context of FOPT and CIPT. Higher order coefficients of the perturbative series, yet unknown, were modelled using available knowledge of the renormalon content of the QCD Adler function. We conclude that within these RGI frameworks some of the moments often employed in αs extractions should be avoided due to their poor perturbative behaviour. Finally, under reasonable assumptions about higher orders, we conclude that FOPT is the preferred method to perform the renormalization group improvement of the perturbative series.

Development of a recursion RNG-based turbulence model

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George; Thangam, S.

1993-01-01

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.

Renormalization group equation analysis of a pseudoscalar portal dark matter model

NASA Astrophysics Data System (ADS)

Ghorbani, Karim

2017-10-01

We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter (DM) model with a Dirac DM candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle θ =6^\\circ , and find the scale of validity in terms of the dark coupling, {λ }d. Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.

Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

NASA Astrophysics Data System (ADS)

Antari, A. El; Zahir, H.; Hasnaoui, A.; Hachem, N.; Alrajhi, A.; Madani, M.; Bouziani, M. El

2018-04-01

Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.

Staggered Orbital Currents in the Half-Filled Two-Leg Ladder

NASA Astrophysics Data System (ADS)

Fjaerestad, J. O.; Marston, Brad; Sudbo, A.

2002-03-01

We present strong analytical and numerical evidence for the existence of a staggered flux (SF) phase in the half-filled two-leg ladder, with true long-range order in the counter-circulating currents. Using abelian bosonization with a careful treatment of the Klein factors, we show that a certain phase of the half-filled ladder, previously identified as having spin-Peierls order, instead exhibits staggered orbital currents with no dimerization.(J. O. Fjærestad and J. B. Marston, cond- mat/0107094.) This result, combined with a weak-coupling renormalization-group analysis, implies that the SF phase exists in a region of the phase diagram of the half-filled t-U-V-J ladder. Using the density-matrix renormalization-group (DMRG) approach generalized to complex-valued wavefunctions, we demonstrate that the SF phase exhibits robust currents at intermediate values of the interaction strengths.

Mutual information, neural networks and the renormalization group

NASA Astrophysics Data System (ADS)

Koch-Janusz, Maciej; Ringel, Zohar

2018-06-01

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

Stiffening of fluid membranes due to thermal undulations: density-matrix renormalization-group study.

PubMed

Nishiyama, Yoshihiro

2002-12-01

It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed the significance of measure factors for the partition sum. Accepting the local curvature as a statistical measure, they found that fluid membranes are stiffened macroscopically. In order to examine this remarkable idea, we performed extensive ab initio simulations for a fluid membrane. We set up a transfer matrix that is diagonalized by means of the density-matrix renormalization group. Our method has an advantage, in that it allows us to survey various statistical measures. As a consequence, we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure. On the contrary, for other measures such as normal displacement and tilt angle, we found a clear tendency toward softening.

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory.

PubMed

Mi, Jianguo; Tang, Yiping; Zhong, Chongli; Li, Yi-Gui

2005-11-03

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.

A new approach for describing glass transition kinetics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasin, N. M.; Shchelkachev, M. G.; Vinokur, V. M.

2010-04-01

We use a functional integral technique generalizing the Keldysh diagram technique to describe glass transition kinetics. We show that the Keldysh functional approach takes the dynamical determinant arising in the glass dynamics into account exactly and generalizes the traditional approach based on using the supersymmetric dynamic generating functional method. In contrast to the supersymmetric method, this approach allows avoiding additional Grassmannian fields and tracking the violation of the fluctuation-dissipation theorem explicitly. We use this method to describe the dynamics of an Edwards-Anderson soft spin-glass-type model near the paramagnet-glass transition. We show that a Vogel-Fulcher-type dynamics arises in the fluctuation regionmore » only if the fluctuation-dissipation theorem is violated in the process of dynamical renormalization of the Keldysh action in the replica space.« less

Stars and (furry) black holes in Lorentz breaking massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Comelli, D.; Nesti, F.; Pilo, L.

We study the exact spherically symmetric solutions in a class of Lorentz-breaking massive gravity theories, using the effective-theory approach where the graviton mass is generated by the interaction with a suitable set of Stueckelberg fields. We find explicitly the exact black-hole solutions which generalizes the familiar Schwarzschild one, which shows a nonanalytic hair in the form of a powerlike term r{sup {gamma}}. For realistic self-gravitating bodies, we find interesting features, linked to the effective violation of the Gauss law: (i) the total gravitational mass appearing in the standard 1/r term gets a multiplicative renormalization proportional to the area of themore » body itself; (ii) the magnitude of the powerlike hairy correction is also linked to size of the body. The novel features can be ascribed to the presence of the Goldstones fluid turned on by matter inside the body; its equation of state approaching that of dark energy near the center. The Goldstones fluid also changes the matter equilibrium pressure, leading to an upper limit for the graviton mass, m < or approx. 10{sup -28/29} eV, derived from the largest stable gravitational bound states in the Universe.« less

Exactly solvable model of the two-dimensional electrical double layer.

PubMed

Samaj, L; Bajnok, Z

2005-12-01

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law.

PubMed

Saichev, A; Sornette, D

2005-05-01

Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Båth's law. Our theory shows that Båth's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +/- 0.1 for Båth's constant value around 1.2, our exact analytical treatment of Båth's law provides new constraints on the productivity exponent alpha and the branching ratio n: 0.9 approximately < alpha < or =1. We propose a method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the "second Båth law for foreshocks:" the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude rho.

Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems

NASA Astrophysics Data System (ADS)

Kais, S.; Bleil, R.

1995-05-01

We develop a systematic way to determine an effective nuclear charge ZRD such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z=2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ˜0.2% for Z=2 to ˜0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N=3-18, Z=3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

PubMed

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Gyeong Won; Shim, Jaewon; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr

The influence of renormalization plasma screening on the entanglement fidelity for the elastic electron-atom scattering is investigated in partially ionized dense hydrogen plasmas. The partial wave analysis and effective interaction potential are employed to obtain the scattering entanglement fidelity in dense hydrogen plasmas as functions of the collision energy, the Debye length, and the renormalization parameter. It is found that the renormalization plasma shielding enhances the scattering entanglement fidelity. Hence, we show that the transmission of the quantum information can be increased about 10% due to the renormalization shielding effect in dense hydrogen plasmas. It is also found that themore » renormalization shielding effect on the entanglement fidelity for the electron-atom collision increases with an increase of the collision energy. In addition, the renormalization shielding function increases with increasing collision energy and saturates to the unity with an increase of the Debye length.« less

Electric Dipole Moment Results from lattice QCD

NASA Astrophysics Data System (ADS)

Dragos, Jack; Luu, Thomas; Shindler, Andrea; de Vries, Jordy

2018-03-01

We utilize the gradient flow to define and calculate electric dipole moments induced by the strong QCD θ-term and the dimension-6 Weinberg operator. The gradient flow is a promising tool to simplify the renormalization pattern of local operators. The results of the nucleon electric dipole moments are calculated on PACS-CS gauge fields (available from the ILDG) using Nf = 2+1, of discrete size 323×64 and spacing a ≃ 0.09 fm. These gauge fields use a renormalization-group improved gauge action and a nonperturbatively O(a) improved clover quark action at β = 1.90, with cSW = 1.715. The calculation is performed at pion masses of mπ ≃ 411, 701 MeV.

Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems

NASA Astrophysics Data System (ADS)

Rück, Marlon; Reuther, Johannes

2018-04-01

We implement an extension of the pseudofermion functional renormalization group method for quantum spin systems that takes into account two-loop diagrammatic contributions. An efficient numerical treatment of the additional terms is achieved within a nested graph construction which recombines different one-loop interaction channels. In order to be fully self-consistent with respect to self-energy corrections, we also include certain three-loop terms of Katanin type. We first apply this formalism to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and benchmark our results against the previous one-loop plus Katanin approach. Even though the renormalization group (RG) equations undergo significant modifications when including the two-loop terms, the magnetic phase diagram, comprising Néel ordered and collinear ordered phases separated by a magnetically disordered regime, remains remarkably unchanged. Only the boundary position between the disordered and the collinear phases is found to be moderately affected by two-loop terms. On the other hand, critical RG scales, which we associate with critical temperatures Tc, are reduced by a factor of ˜2 indicating that the two-loop diagrams play a significant role in enforcing the Mermin-Wagner theorem. Improved estimates for critical temperatures are also obtained for the Heisenberg ferromagnet on the three-dimensional simple cubic lattice where errors in Tc are reduced by ˜34 % . These findings have important implications for the quantum phase diagrams calculated within the previous one-loop plus Katanin approach which turn out to be already well converged.

Renormalization of the Lattice Heavy Quark Classical Velocity

NASA Astrophysics Data System (ADS)

Mandula, Jeffrey E.; Ogilvie, Michael C.

1996-03-01

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the "classical velocity" v becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time — Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using two ensembles of lattices, one at β = 5.7 and the other at β = 6.1 The estimates agree, and indicate that for small classical velocities, ν→ is reduced by about 25-30%.

Renormalization of entanglement entropy from topological terms

NASA Astrophysics Data System (ADS)

Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

2018-05-01

We propose a renormalization scheme for entanglement entropy of three-dimensional CFTs with a four-dimensional asymptotically AdS gravity dual in the context of the gauge/gravity correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. We provide an explicit prescription for the renormalized entanglement entropy, which is derived via the replica trick. This is achieved by considering a Euclidean gravitational action renormalized by the addition of the Chern form at the spacetime boundary, evaluated in the conically-singular replica manifold. We show that the addition of this boundary term cancels the divergent part of the entanglement entropy, recovering the results obtained by Taylor and Woodhead. We comment on how this prescription for renormalizing the entanglement entropy is in line with the general program of topological renormalization in asymptotically AdS gravity.

mr: A C++ library for the matching and running of the Standard Model parameters

NASA Astrophysics Data System (ADS)

Kniehl, Bernd A.; Pikelner, Andrey F.; Veretin, Oleg L.

2016-09-01

We present the C++ program library mr that allows us to reliably calculate the values of the running parameters in the Standard Model at high energy scales. The initial conditions are obtained by relating the running parameters in the MS bar renormalization scheme to observables at lower energies with full two-loop precision. The evolution is then performed in accordance with the renormalization group equations with full three-loop precision. Pure QCD corrections to the matching and running are included through four loops. We also provide a Mathematica interface for this program library. Catalogue identifier: AFAI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 517613 No. of bytes in distributed program, including test data, etc.: 2358729 Distribution format: tar.gz Programming language: C++. Computer: IBM PC. Operating system: Linux, Mac OS X. RAM: 1 GB Classification: 11.1. External routines: TSIL [1], OdeInt [2], boost [3] Nature of problem: The running parameters of the Standard Model renormalized in the MS bar scheme at some high renormalization scale, which is chosen by the user, are evaluated in perturbation theory as precisely as possible in two steps. First, the initial conditions at the electroweak energy scale are evaluated from the Fermi constant GF and the pole masses of the W, Z, and Higgs bosons and the bottom and top quarks including the full two-loop threshold corrections. Second, the evolution to the high energy scale is performed by numerically solving the renormalization group evolution equations through three loops. Pure QCD corrections to the matching and running are included through four loops. Solution method: Numerical integration of analytic expressions Additional comments: Available for download from URL: http://apik.github.io/mr/. The MathLink interface is tested to work with Mathematica 7-9 and, with an additional flag, also with Mathematica 10 under Linux and with Mathematica 10 under Mac OS X. Running time: less than 1 second References: [1] S. P. Martin and D. G. Robertson, Comput. Phys. Commun. 174 (2006) 133-151 [hep-ph/0501132]. [2] K. Ahnert and M. Mulansky, AIP Conf. Proc. 1389 (2011) 1586-1589 [arxiv:1110.3397 [cs.MS

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Chiu, Jui-Yu; Jain, Ambar; Neill, Duff; Rothstein, Ira Z.

2012-05-01

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the relevant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. Such observables include: transverse momentum distributions at p T much less then the high energy scattering scale, jet broadening, exclusive hadroproduction and decay, as well as the Sudakov form factor. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any sce- nario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form fac- tor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are universal. We present details of the factorization and re- summation of the jet broadening cross section including a renormalization in p ⊥ space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal

NASA Astrophysics Data System (ADS)

Krčmár, Roman; Šamaj, Ladislav

2018-01-01

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ηe and δe which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.

Model parameter learning using Kullback-Leibler divergence

NASA Astrophysics Data System (ADS)

Lin, Chungwei; Marks, Tim K.; Pajovic, Milutin; Watanabe, Shinji; Tung, Chih-kuan

2018-02-01

In this paper, we address the following problem: For a given set of spin configurations whose probability distribution is of the Boltzmann type, how do we determine the model coupling parameters? We demonstrate that directly minimizing the Kullback-Leibler divergence is an efficient method. We test this method against the Ising and XY models on the one-dimensional (1D) and two-dimensional (2D) lattices, and provide two estimators to quantify the model quality. We apply this method to two types of problems. First, we apply it to the real-space renormalization group (RG). We find that the obtained RG flow is sufficiently good for determining the phase boundary (within 1% of the exact result) and the critical point, but not accurate enough for critical exponents. The proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the real-space RG procedure. Second, we apply this method to the dynamical system composed of self-propelled particles, where we extract the parameter of a statistical model (a generalized XY model) from a dynamical system described by the Viscek model. We are able to obtain reasonable coupling values corresponding to different noise strengths of the Viscek model. Our method is thus able to provide quantitative analysis of dynamical systems composed of self-propelled particles.

Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator

NASA Astrophysics Data System (ADS)

Allerdt, Andrew; Feiguin, A. E.; Martins, G. B.

2017-07-01

We calculate exact zero-temperature real-space properties of a substitutional magnetic impurity coupled to the edge of a zigzag silicenelike nanoribbon. Using a Lanczos transformation [A. Allerdt et al., Phys. Rev. B 91, 085101 (2015), 10.1103/PhysRevB.91.085101] and the density-matrix renormalization-group method, we obtain a realistic description of stanene and germanene that includes the bulk and the edges as boundary one-dimensional helical metallic states. Our results for substitutional impurities indicate that the development of a Kondo state and the structure of the spin correlations between the impurity and the electron spins in the metallic edge state depend considerably on the location of the impurity. More specifically, our real-space resolution allows us to conclude that there is a sharp distinction between the impurity being located at a crest or a trough site at the zigzag edge. We also observe, as expected, that the spin correlations are anisotropic due to an emerging Dzyaloshinskii-Moriya interaction with the conduction electrons and that the edges scatter from the impurity and "snake" or circle around it. Our estimates for the Kondo temperature indicate that there is a very weak enhancement due to the presence of spin-orbit coupling.

Hopping and the Stokes–Einstein relation breakdown in simple glass formers

PubMed Central

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-01-01

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition—like that of other statistical systems—is exact when the spatial dimension d→∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, d=2,3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses. PMID:25288722

Localization Protection and Symmetry Breaking in One-dimensional Potts Chains

NASA Astrophysics Data System (ADS)

Friedman, Aaron; Vasseur, Romain; Potter, Andrew; Parameswaran, Siddharth

Recent work on the 3-state Potts and Z3 clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited states by many-body localization (MBL). However, the Potts model has a non-Abelian S3 symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups (Z2 or Z3), with the topological phase corresponding to broken Z3 symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either Z3 or Z2 symmetry, forbidden within Landau theory. NSF DGE-1321846 (AJF), NSF DMR-1455366 and President's Research Catalyst Award No. CA-15-327861 from the University of California Office of the President (SAP), LDRD Program of LBNL (RV), NSF PHY11-25915 at the KITP (AJF, RV, SAP).

A minimal model for the structural energetics of VO2

NASA Astrophysics Data System (ADS)

Kim, Chanul; Marianetti, Chris; The Marianetti Group Team

Resolving the structural, magnetic, and electronic structure of VO2 from the first-principles of quantum mechanics is still a forefront problem despite decades of attention. Hybrid functionals have been shown to qualitatively ruin the structural energetics. While density functional theory (DFT) combined with cluster extensions of dynamical mean-field theory (DMFT) have demonstrated promising results in terms of the electronic properties, structural phase stability has not yet been addressed. In order to capture the basic physics of the structural transition, we propose a minimal model of VO2 based on the one dimensional Peierls-Hubbard model and parameterize this based on DFT calculations of VO2. The total energy versus dimerization in the minimal mode is then solved numerically exactly using density matrix renormalization group (DMRG) and compared to the Hartree-Fock solution. We demonstrate that the Hartree-Fock solution exhibits the same pathologies as DFT+U, and spin density functional theory for that matter, while the DMRG solution is consistent with experimental observation. Our results demonstrate the critical role of non-locality in the total energy, and this will need to be accounted for to obtain a complete description of VO2 from first-principles. The authors acknowledge support from FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-10-21

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

Engineering electronic states of periodic and quasiperiodic chains by buckling

NASA Astrophysics Data System (ADS)

Mukherjee, Amrita; Nandy, Atanu; Chakrabarti, Arunava

2017-07-01

The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non-uniform, quasiperiodic manner is investigated within a tight binding formalism. We have addressed two specific cases, viz., a perfectly periodic chain wrinkled in a quasiperiodic Fibonacci pattern, and a quasiperiodic Fibonacci chain, where the buckling also takes place in a Fibonacci pattern. The buckling brings distant neighbors in the parent chain to close proximity, which is simulated by a tunnel hopping amplitude. It is seen that, in the perfectly ordered case, increasing the strength of the tunnel hopping (that is, bending the segments more) absolutely continuous density of states is retained towards the edges of the band, while the central portion becomes fragmented and host subbands of narrowing widths containing extended, current carrying states, and multiple isolated bound states formed as a result of the bending. A switching ;on; and ;off; of the electronic transmission can thus be engineered by buckling. On the other hand, in the second example of a quasiperiodic Fibonacci chain, imparting a quasiperiodic buckling is found to generate continuous subband(s) destroying the usual multifractality of the energy spectrum. We present exact results based on a real space renormalization group analysis, that is corroborated by explicit calculation of the two terminal electronic transport.

Superuniversal transport near a (2 +1 ) -dimensional quantum critical point

NASA Astrophysics Data System (ADS)

Rose, F.; Dupuis, N.

2017-09-01

We compute the zero-temperature conductivity in the two-dimensional quantum O (N ) model using a nonperturbative functional renormalization-group approach. At the quantum critical point we find a universal conductivity σ*/σQ (with σQ=q2/h the quantum of conductance and q the charge) in reasonable quantitative agreement with quantum Monte Carlo simulations and conformal bootstrap results. In the ordered phase the conductivity tensor is defined, when N ≥3 , by two independent elements, σA(ω ) and σB(ω ) , respectively associated with SO (N ) rotations which do and do not change the direction of the order parameter. Whereas σA(ω →0 ) corresponds to the response of a superfluid (or perfect inductance), the numerical solution of the flow equations shows that limω→0σB(ω ) /σQ=σB*/σQ is a superuniversal (i.e., N -independent) constant. These numerical results, as well as the known exact value σB*/σQ=π /8 in the large-N limit, allow us to conjecture that σB*/σQ=π /8 holds for all values of N , a result that can be understood as a consequence of gauge invariance and asymptotic freedom of the Goldstone bosons in the low-energy limit.

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Drivas, Theodore D.

2018-02-01

We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and Péclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur via two mechanisms: an anomalous input of negative entropy (negentropy) by pressure work and a cascade of negentropy to small scales. We derive "4 /5 th-law"-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the "Big Power Law in the Sky" observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade or an inverse cascade of usual thermodynamic entropy.

Structural impact on the eigenenergy renormalization for carbon and silicon allotropes and boron nitride polymorphs

NASA Astrophysics Data System (ADS)

Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang

2018-05-01

The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.

Aspects of Galileon non-renormalization

DOE PAGES

Goon, Garrett; Hinterbichler, Kurt; Joyce, Austin; ...

2016-11-18

We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and P ( X) theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. Furthermore, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.

Composite operator and condensate in the S U (N ) Yang-Mills theory with U (N -1 ) stability group

NASA Astrophysics Data System (ADS)

Warschinke, Matthias; Matsudo, Ryutaro; Nishino, Shogo; Shinohara, Toru; Kondo, Kei-Ichi

2018-02-01

Recently, some reformulations of the Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition have been developed in order to understand confinement from the viewpoint of the dual superconductivity. In this paper we focus on the reformulated S U (N ) Yang-Mills theory in the minimal option with U (N -1 ) stability group. Despite existing numerical simulations on the lattice we perform the perturbative analysis to one-loop level as a first step towards the nonperturbative analytical treatment. First, we give the Feynman rules and calculate all renormalization factors to obtain the standard renormalization group functions to one-loop level in light of the renormalizability of this theory. Then we introduce a mixed gluon-ghost composite operator of mass dimension 2 and show the Bechi-Rouet-Stora-Tyutin invariance and the multiplicative renormalizability. Armed with these results, we argue the existence of the mixed gluon-ghost condensate by means of the so-called local composite operator formalism, which leads to various interesting implications for confinement as shown in preceding works.

Nonperturbative Renormalization Group Approach to Polymerized Membranes

NASA Astrophysics Data System (ADS)

Essafi, Karim; Kownacki, Jean-Philippe; Mouhanna, Dominique

2014-03-01

Membranes or membrane-like materials play an important role in many fields ranging from biology to physics. These systems form a very rich domain in statistical physics. The interplay between geometry and thermal fluctuations lead to exciting phases such flat, tubular and disordered flat phases. Roughly speaking, membranes can be divided into two group: fluid membranes in which the molecules are free to diffuse and thus no shear modulus. On the other hand, in polymerized membranes the connectivity is fixed which leads to elastic forces. This difference between fluid and polymerized membranes leads to a difference in their critical behaviour. For instance, fluid membranes are always crumpled, whereas polymerized membranes exhibit a phase transition between a crumpled phase and a flat phase. In this talk, I will focus only on polymerized phantom, i.e. non-self-avoiding, membranes. The critical behaviour of both isotropic and anisotropic polymerized membranes are studied using a nonperturbative renormalization group approach (NPRG). This allows for the investigation of the phase transitions and the low temperature flat phase in any internal dimension D and embedding d. Interestingly, graphene behaves just as a polymerized membrane in its flat phase.

Type 0 open string amplitudes and the tensionless limit

NASA Astrophysics Data System (ADS)

Rojas, Francisco

2014-12-01

The sum over planar multiloop diagrams in the NS + sector of type 0 open strings in flat spacetime has been proposed by Thorn as a candidate to resolve nonperturbative issues of gauge theories in the large N limit. With S U (N ) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the 't Hooft limit N →∞ with N gs2 held fixed. By including only planar diagrams in the sum the usual mechanism for the cancellation of loop divergences (which occurs, for example, among the planar and Möbius strip diagrams by choosing a specific gauge group) is not available and a renormalization procedure is needed. In this article the renormalization is achieved by suspending total momentum conservation by an amount p ≡∑ i n ki≠0 at the level of the integrands in the integrals over the moduli and analytically continuing them to p =0 at the very end. This procedure has been successfully tested for the 2 and 3 gluon planar loop amplitudes by Thorn. Gauge invariance is respected and the correct running of the coupling in the limiting gauge field theory was also correctly obtained. In this article we extend those results in two directions. First, we generalize the renormalization method to an arbitrary n -gluon planar loop amplitude giving full details for the 4-point case. One of our main results is to provide a fully renormalized amplitude which is free of both UV and the usual spurious divergences leaving only the physical singularities in it. Second, using the complete renormalized amplitude, we extract the high-energy scattering regime at fixed angle (tensionless limit). Apart from obtaining the usual exponential falloff at high energies, we compute the full dependence on the scattering angle which shows the existence of a smooth connection between the Regge and hard scattering regimes.

Fractional Stochastic Field Theory

NASA Astrophysics Data System (ADS)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

On the robustness of the primordial power spectrum in renormalized Higgs inflation

NASA Astrophysics Data System (ADS)

Bezrukov, Fedor; Pauly, Martin; Rubio, Javier

2018-02-01

We study the cosmological consequences of higher-dimensional operators respecting the asymptotic symmetries of the tree-level Higgs inflation action. The main contribution of these operators to the renormalization group enhanced potential is localized in a compact field range, whose upper limit is close to the end of inflation. The spectrum of primordial fluctuations in the so-called universal regime turns out to be almost insensitive to radiative corrections and in excellent agreement with the present cosmological data. However, higher-dimensional operators can play an important role in critical Higgs inflation scenarios containing a quasi-inflection point along the inflationary trajectory. The interplay of radiative corrections with this quasi-inflection point may translate into a sizable modification of the inflationary observables.

Environmentally sensitive theory of electronic and optical transitions in atomically thin semiconductors

NASA Astrophysics Data System (ADS)

Cho, Yeongsu; Berkelbach, Timothy C.

2018-01-01

We present an electrostatic theory of band-gap renormalization in atomically thin semiconductors that captures the strong sensitivity to the surrounding dielectric environment. In particular, our theory aims to correct known band gaps, such as that of the three-dimensional bulk crystal. Combining our quasiparticle band gaps with an effective-mass theory of excitons yields environmentally sensitive optical gaps as would be observed in absorption or photoluminescence. For an isolated monolayer of MoS2, the presented theory is in good agreement with ab initio results based on the G W approximation and the Bethe-Salpeter equation. We find that changes in the electronic band gap are almost exactly offset by changes in the exciton binding energy such that the energy of the first optical transition is nearly independent of the electrostatic environment, rationalizing experimental observations.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Virtual Petaflop Simulation: Parallel Potential Solvers and New Integrators for Gravitational Systems

NASA Technical Reports Server (NTRS)

Lake, George; Quinn, Thomas; Richardson, Derek C.; Stadel, Joachim

1999-01-01

"The orbit of any one planet depends on the combined motion of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect" -Isaac Newton 1687. Epochal surveys are throwing down the gauntlet for cosmological simulation. We describe three keys to meeting the challenge of N-body simulation: adaptive potential solvers, adaptive integrators and volume renormalization. With these techniques and a dedicated Teraflop facility, simulation can stay even with observation of the Universe. We also describe some problems in the formation and stability of planetary systems. Here, the challenge is to perform accurate integrations that retain Hamiltonian properties for 10(exp 13) timesteps.

Repeated Structural Imaging Reveals Nonlinear Progression of Experience-Dependent Volume Changes in Human Motor Cortex.

PubMed

Wenger, Elisabeth; Kühn, Simone; Verrel, Julius; Mårtensson, Johan; Bodammer, Nils Christian; Lindenberger, Ulman; Lövdén, Martin

2017-05-01

Evidence for experience-dependent structural brain change in adult humans is accumulating. However, its time course is not well understood, as intervention studies typically consist of only 2 imaging sessions (before vs. after training). We acquired up to 18 structural magnetic resonance images over a 7-week period while 15 right-handed participants practiced left-hand writing and drawing. After 4 weeks, we observed increases in gray matter of both left and right primary motor cortices relative to a control group; 3 weeks later, these differences were no longer reliable. Time-series analyses revealed that gray matter in the primary motor cortices expanded during the first 4 weeks and then partially renormalized, in particular in the right hemisphere, despite continued practice and increasing task proficiency. Similar patterns of expansion followed by partial renormalization are also found in synaptogenesis, cortical map plasticity, and maturation, and may qualify as a general principle of structural plasticity. Research on human brain plasticity needs to encompass more than 2 measurement occasions to capture expansion and potential renormalization processes over time. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Normal state of metallic hydrogen sulfide

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Kutukov, A. A.; Mazur, E. A.

2017-02-01

A generalized theory of the normal properties of metals in the case of electron-phonon (EP) systems with a nonconstant density of electron states has been used to study the normal state of the SH3 and SH2 phases of hydrogen sulfide at different pressures. The frequency dependence of the real Re Σ (ω) and imaginary ImΣ (ω) parts of the self-energy Σ (ω) part (SEP) of the Green's function of the electron Σ (ω), real part Re Z (ω), and imaginary part Im Z (ω) of the complex renormalization of the mass of the electron; the real part Re χ (ω) and the imaginary part Imχ (ω) of the complex renormalization of the chemical potential; and the density of electron states N (ɛ) renormalized by strong electron-phonon interaction have been calculated. Calculations have been carried out for the stable orthorhombic structure (space group Im3¯ m) of the hydrogen sulfide SH3 for three values of the pressure P = 170, 180, and 225 GPa; and for an SH2 structure with a symmetry of I4/ mmm ( D4 h1¯7) for three values of pressure P = 150, 180, and 225 GP at temperature T = 200 K.

Renormalization scheme dependence of the two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM.

PubMed

Borowka, S; Hahn, T; Heinemeyer, S; Heinrich, G; Hollik, W

Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass, [Formula: see text], at the level of the current experimental precision requires the inclusion of momentum-dependent contributions at the two-loop level. Recently two groups presented the two-loop QCD momentum-dependent corrections to [Formula: see text] (Borowka et al., Eur Phys J C 74(8):2994, 2014; Degrassi et al., Eur Phys J C 75(2):61, 2015), using a hybrid on-shell-[Formula: see text] scheme, with apparently different results. We show that the differences can be traced back to a different renormalization of the top-quark mass, and that the claim in Ref. Degrassi et al. (Eur Phys J C 75(2):61, 2015) of an inconsistency in Ref. Borowka et al. (Eur Phys J C 74(8):2994, 2014) is incorrect. We furthermore compare consistently the results for [Formula: see text] obtained with the top-quark mass renormalized on-shell and [Formula: see text]. The latter calculation has been added to the FeynHiggs package and can be used to estimate missing higher-order corrections beyond the two-loop level.

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Throckmorton, Robert; Hofmann, Johannes; Barnes, Edwin

We develop a theory for electron-electron interaction-induced many-body effects in three dimensional (3D) Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group (RG) flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies non-monotonically as the low-energy, non-interacting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number relative to the leading-order result. Supported by LPS-MPO-CMTC.

Scale-invariant feature extraction of neural network and renormalization group flow

NASA Astrophysics Data System (ADS)

Iso, Satoshi; Shiba, Shotaro; Yokoo, Sumito

2018-05-01

Theoretical understanding of how a deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse graining. It reminds us of the basic renormalization group (RG) concept in statistical physics. In order to explore possible relations between DNN and RG, we use the restricted Boltzmann machine (RBM) applied to an Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from T =0 to T =6 generates a flow along which the temperature approaches the critical value Tc=2.2 7 . This behavior is the opposite of the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards Tc and how the RBM learns to extract features of spin configurations.

Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

NASA Astrophysics Data System (ADS)

Chen, Guang-Hong; Wu, Yong-Shi

2002-02-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents νm and βk, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.

An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hannon, Kevin P.; Li, Chenyang; Evangelista, Francesco A., E-mail: francesco.evangelista@emory.edu

2016-05-28

We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller–Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (Δ{sub ST}) of the naphthyne isomers strongly depend onmore » the equilibrium structures. For a consistent set of geometries, the Δ{sub ST} values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.« less

Ghost-gluon vertex in the presence of the Gribov horizon

NASA Astrophysics Data System (ADS)

Mintz, B. W.; Palhares, L. F.; Sorella, S. P.; Pereira, A. D.

2018-02-01

We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov-Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice Yang-Mills simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the renormalization group-improved Curci-Ferrari model.

The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

NASA Astrophysics Data System (ADS)

Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter

2014-06-01

In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.

Asymptotically free theory with scale invariant thermodynamics

NASA Astrophysics Data System (ADS)

Ferrari, Gabriel N.; Kneur, Jean-Loïc; Pinto, Marcus Benghi; Ramos, Rudnei O.

2017-12-01

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasiparticle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

A low-cost approach to electronic excitation energies based on the driven similarity renormalization group

NASA Astrophysics Data System (ADS)

Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.

2017-08-01

We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

PubMed

Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo

2018-01-18

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Wilsonian Renormalization Group and the Lippmann-Schwinger Equation with a Multitude of Cutoff Parameters

NASA Astrophysics Data System (ADS)

Epelbaum, E.; Gegelia, J.; Meißner, Ulf-G.

2018-03-01

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed. Supported in part by BMBF under Grant No. 05P2015 - NUSTAR R&D), DFG and NSFC through Funds Provided to the Sino- German CRC 110 “Symmetries and the Emergence of Structure in QCD”, National Natural Science Foundation of China under Grant No. 11621131001, DFG Grant No. TRR110, the Georgian Shota Rustaveli National Science Foundation (grant FR/417/6-100/14) and the CAS President’s International Fellowship Initiative (PIFI) under Grant No. 2017VMA0025

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

NASA Astrophysics Data System (ADS)

Fugger, Delia M.; Dorda, Antonius; Schwarz, Frauke; von Delft, Jan; Arrigoni, Enrico

2018-01-01

We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B. We investigate the interplay between the shift ({ω }B) of the Kondo peak in the spin-resolved density of states (DOS) and the one ({φ }B) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as {φ }B only for | g| {μ }BB\\gg {k}B{T}K. Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.

The signed permutation group on Feynman graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purkart, Julian, E-mail: purkart@physik.hu-berlin.de

2016-08-15

The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization schememore » and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.« less

Renormalization-group theory for finite-size scaling in extreme statistics

NASA Astrophysics Data System (ADS)

Györgyi, G.; Moloney, N. R.; Ozogány, K.; Rácz, Z.; Droz, M.

2010-04-01

We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.

A state interaction spin-orbit coupling density matrix renormalization group method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe{submore » 2}S{sub 2}(SCH{sub 3}){sub 4}]{sup 3−}, determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.« less

Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS..

NASA Astrophysics Data System (ADS)

Siegel, J.; Siegel, Edward Carl-Ludwig

2011-03-01

Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

Functional renormalization group and bosonization as a solver for 2D fermionic Hubbard models

NASA Astrophysics Data System (ADS)

Schuetz, Florian; Marston, Brad

2007-03-01

The functional renormalization group (fRG) provides an unbiased framework to analyze competing instabilities in two-dimensional electron systems and has been used extensively over the past decade [1]. In order to obtain an equally unbiased tool to interprete the flow, we investigate the combination of a many-patch, one-loop calculation with higher dimensional bosonization [2] of the resulting low-energy action. Subsequently a semi-classical approximation [3] can be used to describe the resulting phases. The spinless Hubbard model on a square lattice with nearest neighbor repulsion is investigated as a test case. [1] M. Salmhofer and C. Honerkamp, Prog. Theor. Phys. 105, 1 (2001). [2] A. Houghton, H.-J. Kwon, J. B. Marston, Adv.Phys. 49, 141 (2000); P. Kopietz, Bosonization of interacting fermions in arbitrary dimensions, (Springer, Berlin, 1997). [3] H.-H. Lin, L. Balents, M. P. A. Fisher, Phys. Rev. B 56, 6569 6593 (1997); J. O. Fjaerestad, J. B. Marston, U. Schollwoeck, Ann. Phys. (N.Y.) 321, 894 (2006).

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

NASA Technical Reports Server (NTRS)

Yakhot, A.; Staroselsky, I.; Orszag, S. A.

1994-01-01

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Global phase diagram of the spinless Falicov-Kimball model in d = 3 : renormalization-group theory

NASA Astrophysics Data System (ADS)

Sariyer, Ozan S.; Hinczewski, Michael; Berker, A. Nihat

2011-03-01

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The phase boundaries are second order, except for an intermediate interaction regime, where a first-order phase boundary between two CO phases occurs. The first-order phase boundary is delimited by special bicritical points. The cross-sections of the global phase diagram with respect to the chemical potentials of the localized and mobile electrons, at all representative interaction and hopping strengths, are calculated and exhibit three distinct topologies. The phase diagrams with respect to electron densities are also calculated. This research was supported by the Alexander von Humboldt Foundation, the Scientific and Technological Research Council of Turkey (TÜBITAK), and the Academy of Sciences of Turkey.

Renormalization group scale-setting from the action—a road to modified gravity theories

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2012-12-01

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Effective electrostatic interactions among charged thermo-responsive microgels immersed in a simple electrolyte

DOE Office of Scientific and Technical Information (OSTI.GOV)

González-Mozuelos, P.

This work explores the nature and thermodynamic behavior of the effective electrostatic interactions among charged microgels immersed in a simple electrolyte, taking special interest in the effects due to the thermally induced variation of the microgel size while the remaining parameters (microgel charge and concentration, plus the amount of added salt) are kept constant. To this end, the rigorous approach obtained from applying the precise methodology of the dressed ion theory to the proper definition of the effective direct correlation functions, which emerge from tracing-out the degrees of freedom of the microscopic ions, is employed to provide an exact descriptionmore » of the parameters characterizing such interactions: screening length, effective permittivity, and renormalized charges. A model solution with three components is assumed: large permeable anionic spheres for the microgels, plus small charged hard spheres of equal size for the monovalent cations and anions. The two-body correlations among the components of this model suspension, used as the input for the determination of the effective interaction parameters, are here calculated by using the hyper-netted chain approximation. It is then found that at finite microgel concentrations the values of these parameters change as the microgel size increases, even though the ionic strength of the supporting electrolyte and the bare charge of the microgels remain fixed during this process. The variation of the screening length, as well as that of the effective permittivity, is rather small, but still interesting in view of the fact that the corresponding Debye length stays constant. The renormalized charges, in contrast, increase markedly as the microgels swell. The ratio of the renormalized charge to the corresponding analytic result obtained in the context of an extended linear response theory allows us to introduce an effective charge that accounts for the non-linear effects induced by the short-ranged association of microions to the microgels. The behavior of these effective charges as a function of the amount of added salt and the macroion charge, size, and concentration reveals the interplay among all these system parameters.« less

On the interface between perturbative and nonperturbative QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deur, Alexandre; Brodsky, Stanley J.; de Teramond, Guy F.

2016-04-04

The QCD running couplingmore » $$\\alpha_s(Q^2)$$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $$\\alpha_s(Q^2)$$. The high-$Q^2$ dependence of the coupling $$\\alpha_s(Q^2)$$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of $$\\alpha_s(Q^2)$$ then determines the scale $$Q_0$$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $$Q_0$$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of $$Q_0$$ and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the $$\\bar{MS}$$, $$g_1$$, $MOM$ and $V$ renormalization schemes. Our results show that the discrepancies on the value of $$\\alpha_s$$ at large distance seen in the literature can be explained by different choices of renormalization schemes. Lastly, we also provide the formulae to compute $$\\alpha_s(Q^2)$$ over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.« less

Topological terms, AdS2 n gravity, and renormalized entanglement entropy of holographic CFTs

NASA Astrophysics Data System (ADS)

Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

2018-05-01

We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS /CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2 n -dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

Classical closure theory and Lam's interpretation of epsilon-RNG

NASA Technical Reports Server (NTRS)

Zhou, YE

1995-01-01

Lam's phenomenological epsilon-renormalization group (RNG) model is quite different from the other members of that group. It does not make use of the correspondence principle and the epsilon-expansion procedure. We demonstrate that Lam's epsilon-RNG model is essentially the physical space version of the classical closure theory in spectral space and consider the corresponding treatment of the eddy viscosity and energy backscatter.

Solar System and stellar tests of a quantum-corrected gravity

NASA Astrophysics Data System (ADS)

Zhao, Shan-Shan; Xie, Yi

2015-09-01

The renormalization group running of the gravitational constant has a universal form and represents a possible extension of general relativity. These renormalization group effects on general relativity will cause the running of the gravitational constant, and there exists a scale of renormalization α ν , which depends on the mass of an astronomical system and needs to be determined by observations. We test renormalization group effects on general relativity and obtain the upper bounds of α ν in the low-mass scales: the Solar System and five systems of binary pulsars. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain new upper bounds on α ν in the Solar System when the Lense-Thirring effect due to the Sun's angular momentum and the uncertainty of the Sun's quadrupole moment are properly taken into account. These two factors were absent in the previous work. We find that INPOP10a yields the upper bound as α ν =(0.3 ±2.8 )×10-20 while EPM2011 gives α ν =(-2.5 ±8.3 )×10-21. Both of them are tighter than the previous result by 4 orders of magnitude. Furthermore, based on the observational data sets of five systems of binary pulsars: PSR J 0737 -3039 , PSR B 1534 +12 , PSR J 1756 -2251 , PSR B 1913 +16 , and PSR B 2127 +11 C , the upper bound is found as α ν =(-2.6 ±5.1 )×10-17. From the bounds of this work at a low-mass scale and the ones at the mass scale of galaxies, we might catch an updated glimpse of the mass dependence of α ν , and it is found that our improvement of the upper bounds in the Solar System can significantly change the possible pattern of the relation between log |α ν | and log m from a linear one to a power law, where m is the mass of an astronomical system. This suggests that |α ν | needs to be suppressed more rapidly with the decrease of the mass of low-mass systems. It also predicts that |α ν | might have an upper limit in high-mass astrophysical systems, which can be tested in the future.

Generalized exact holographic mapping with wavelets

NASA Astrophysics Data System (ADS)

Lee, Ching Hua

2017-12-01

The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.

Renormalization of the inflationary perturbations revisited

NASA Astrophysics Data System (ADS)

Markkanen, Tommi

2018-05-01

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

Minimally doubled fermions at one loop

NASA Astrophysics Data System (ADS)

Capitani, Stefano; Weber, Johannes; Wittig, Hartmut

2009-10-01

Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which is linearly divergent. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one.

Temperature and frequency dependent mean free paths of renormalized phonons in nonlinear lattices

NASA Astrophysics Data System (ADS)

Li, Nianbei; Liu, Junjie; Wu, Changqin; Li, Baowen

2018-02-01

Unraveling general properties of renormalized phonons are of fundamental relevance to the heat transport in the regime of strong nonlinearity. In this work, we directly study the temperature and frequency dependent mean free path (MFP) of renormalized phonons with the newly developed numerical tuning fork method. The typical 1D nonlinear lattices such as Fermi-Pasta-Ulam β lattice and {φ }4 lattice are investigated in detail. Interestingly, it is found that the MFPs are inversely proportional to the frequencies of renormalized phonons rather than the square of phonon frequencies predicted by existing phonon scattering theory.

Entanglement entropy in a boundary impurity model.

PubMed

Levine, G C

2004-12-31

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

The metric on field space, functional renormalization, and metric–torsion quantum gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reuter, Martin, E-mail: reuter@thep.physik.uni-mainz.de; Schollmeyer, Gregor M., E-mail: schollmeyer@thep.physik.uni-mainz.de

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modifiedmore » FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.« less

Gutzwiller renormalization group

DOE PAGES

Lanatà, Nicola; Yao, Yong -Xin; Deng, Xiaoyu; ...

2016-01-06

We develop a variational scheme called the “Gutzwiller renormalization group” (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. Furthermore, we perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG mightmore » enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.« less

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

NASA Astrophysics Data System (ADS)

Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

2018-03-01

Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene

NASA Astrophysics Data System (ADS)

Leblanc, J. P. F.; Carbotte, J. P.; Nicol, E. J.

2012-02-01

Motivated by recent tunneling and angle-resolved photoemission (ARPES) work [1,2], we explore the combined effect of electron-electron and electron-phonon couplings on the renormalized energy dispersion, the spectral function, and the density of states of doped graphene. We find that the plasmarons seen in ARPES are also observable in the density of states and appear as structures with quadratic dependence on energy about the minima. Further, we illustrate how knowledge of the slopes of both the density of states and the renormalized dispersion near the Fermi level can allow for the separation of momentum and frequency dependent renormalizations to the Fermi velocity. This analysis should allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction. [4pt] [1] Brar et al. Phys. Rev. Lett. 104, 036805 (2010) [2] Bostwick et al. Science 328, p.999 (2010)

Comment on ``Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of-Equilibrium Systems''

NASA Astrophysics Data System (ADS)

Luo, H. G.; Xiang, T.; Wang, X. Q.

2003-07-01

A Comment on the Letter by

Structure of rapidity divergences in multi-parton scattering soft factors

NASA Astrophysics Data System (ADS)

Vladimirov, Alexey

2018-04-01

We discuss the structure of rapidity divergences that are presented in the soft factors of transverse momentum dependent (TMD) factorization theorems. To provide the discussion on the most general level we consider soft factors for multi-parton scattering. We show that the rapidity divergences are result of the gluon exchanges with the distant transverse plane, and are structurally equivalent to the ultraviolet divergences. It allows to formulate and to prove the renormalization theorem for rapidity divergences. The proof is made with the help the conformal transformation which maps rapidity divergences to ultraviolet divergences. The theorem is the systematic form of the factorization of rapidity divergences, which is required for the definition of TMD parton distributions. In particular, the definition of multi parton distributions is presented. The equivalence of ultraviolet and rapidity divergences leads to the exact relation between soft and rapidity anomalous dimensions. Using this relation we derive the rapidity anomalous dimension at the three-loop order.

Quantum properties of supersymmetric theories regularized by higher covariant derivatives

NASA Astrophysics Data System (ADS)

Stepanyantz, Konstantin

2018-02-01

We investigate quantum corrections in \\mathscr{N} = 1 non-Abelian supersymmetric gauge theories, regularized by higher covariant derivatives. In particular, by the help of the Slavnov-Taylor identities we prove that the vertices with two ghost legs and one leg of the quantum gauge superfield are finite in all orders. This non-renormalization theorem is confirmed by an explicit one-loop calculation. By the help of this theorem we rewrite the exact NSVZ β-function in the form of the relation between the β-function and the anomalous dimensions of the matter superfields, of the quantum gauge superfield, and of the Faddeev-Popov ghosts. Such a relation has simple qualitative interpretation and allows suggesting a prescription producing the NSVZ scheme in all loops for the theories regularized by higher derivatives. This prescription is verified by the explicit three-loop calculation for the terms quartic in the Yukawa couplings.

Using nonequilibrium dynamics to probe competing orders in a Mott-Peierls system

DOE PAGES

Wang, Y.; Moritz, B.; Chen, C. -C.; ...

2016-02-24

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softeningmore » due to a stronger coupling near k F. As a result, this behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.« less

Asymptotically Free Gauge Theories. I

DOE R&D Accomplishments Database

Wilczek, Frank; Gross, David J.

1973-07-01

Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

Spacetime Symmetries and Conformal Data in the Continuous Multiscale Entanglement Renormalization Ansatz

NASA Astrophysics Data System (ADS)

Hu, Q.; Vidal, G.

2017-07-01

The generalization of the multiscale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013), 10.1103/PhysRevLett.110.100402], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this Letter, we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state |ΨΛ⟩ with finite UV cutoff Λ can capture the spacetime symmetries of the ground state |Ψ ⟩. For a free boson conformal field theory (CFT) in 1 +1 dimensions, as a concrete example, we build a quasilocal unitary transformation V that maps |Ψ ⟩ into |ΨΛ⟩ and show two main results. (i) Any spacetime symmetry of the ground state |Ψ ⟩ is also mapped by V into a spacetime symmetry of the cMERA |ΨΛ⟩. However, while in the CFT, the stress-energy tensor Tμ ν(x ) (in terms of which all the spacetime symmetry generators are expressed) is local, and the corresponding cMERA stress-energy tensor Tμν Λ(x )=V Tμ ν(x )V† is quasilocal. (ii) From the cMERA, we can extract quasilocal scaling operators OαΛ(x ) characterized by the exact same scaling dimensions Δα, conformal spins sα, operator product expansion coefficients Cα β γ, and central charge c as the original CFT. Finally, we argue that these results should also apply to interacting theories.

Nonequilibrium self-energies, Ng approach, and heat current of a nanodevice for small bias voltage and temperature

NASA Astrophysics Data System (ADS)

Aligia, A. A.

2014-03-01

Using nonequilibrium renormalized perturbation theory to second order in the renormalized Coulomb repulsion, we calculate the lesser Σ< and and greater Σ> self-energies of the impurity Anderson model, which describes the current through a quantum dot, in the general asymmetric case. While in general a numerical integration is required to evaluate the perturbative result, we derive an analytical approximation for small frequency ω, bias voltage V, and temperature T, which is exact to total second order in these quantities. The approximation is valid when the corresponding energies ℏω, eV, and kBT are small compared to kBTK, where TK is the Kondo temperature. The result of the numerical integration is compared with the analytical one and with Ng approximation, in which Σ< and Σ> are assumed proportional to the retarded self-energy Σr times an average Fermi function. While it fails at T =0 for ℏ |ω|≲eV, we find that the Ng approximation is excellent for kBT>eV/2 and improves for asymmetric coupling to the leads. Even at T =0, the effect of the Ng approximation on the total occupation at the dot is very small. The dependence on ω and V are discussed in comparison with a Ward identity that is fulfilled by the three approaches. We also calculate the heat currents between the dot and any of the leads at finite bias voltage. One of the heat currents changes sign with the applied bias voltage at finite temperature.

Bose gases near resonance: Renormalized interactions in a condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Fei, E-mail: feizhou@phas.ubc.ca; Mashayekhi, Mohammad S.

2013-01-15

Bose gases at large scattering lengths or beyond the usual dilute limit for a long time have been one of the most challenging problems in many-body physics. In this article, we investigate the fundamental properties of a near-resonance Bose gas and illustrate that three-dimensional Bose gases become nearly fermionized near resonance when the chemical potential as a function of scattering lengths reaches a maximum and the atomic condensates lose metastability. The instability and accompanying maximum are shown to be a precursor of the sign change of g{sub 2}, the renormalized two-body interaction between condensed atoms. g{sub 2} changes from effectivelymore » repulsive to attractive when approaching resonance from the molecular side, even though the scattering length is still positive. This occurs when dimers, under the influence of condensates, emerge at zero energy in the atomic gases at a finite positive scattering length. We carry out our studies of Bose gases via applying a self-consistent renormalization group equation which is further subject to a boundary condition. We also comment on the relation between the approach here and the diagrammatic calculation in an early article [D. Borzov, M.S. Mashayekhi, S. Zhang, J.-L. Song, F. Zhou, Phys. Rev. A 85 (2012) 023620]. - Highlights: Black-Right-Pointing-Pointer A Bose gas becomes nearly fermionized when its chemical potential approaches a maximum near resonance. Black-Right-Pointing-Pointer At the maximum, an onset instability sets in at a positive scattering length. Black-Right-Pointing-Pointer Condensates strongly influence the renormalization flow of few-body running coupling constants. Black-Right-Pointing-Pointer The effective two-body interaction constant changes its sign at a positive scattering length.« less

A Non-Perturbative Treatment of Quantum Impurity Problems in Real Lattices

NASA Astrophysics Data System (ADS)

Allerdt, Andrew C.

Historically, the RKKY or indirect exchange, interaction has been accepted as being able to be described by second order perturbation theory. A typical universal expression is usually given in this context. This approach, however, fails to incorporate many body effects, quantum fluctuations, and other important details. In Chapter 2, a novel numerical approach is developed to tackle these problems in a quasi-exact, non-perturbative manner. Behind the method lies the main concept of being able to exactly map an n-dimensional lattice problem onto a 1-dimensional chain. The density matrix renormalization group algorithm is then employed to solve the newly cast Hamiltonian. In the following chapters, it is demonstrated that conventional RKKY theory does not capture the crucial physics. It is found that the Kondo effect, i.e. the screening of an impurity spin, tends to dominate over a ferromagnetic interaction between impurity spins. Furthermore, it is found that the indirect exchange interaction does not decay algebraically. Instead, there is a crossover upon increasing JK, where impurities favor forming their own independent Kondo states after just a few lattice spacings. This is not a trivial result, as one may naively expect impurities to interact when their conventional Kondo clouds overlap. The spin structure around impurities coupled to the edge of a 2D topological insulator is investigated in Chapter 7. Modeled after materials such as silicine, germanene, and stanene, it is shown with spatial resolution of the lattice that the specific impurity placement plays a key role. Effects of spin-orbit interactions are also discussed. Finally, in the last chapter, transition metal complexes are studied. This really shows the power and versatility of the method developed throughout the work. The spin states of an iron atom in the molecule FeN4C 10 are calculated and compared to DFT, showing the importance of inter-orbital coulomb interactions. Using dynamical DMRG, the density of states for the 3d-orbitals can also be obtained.

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

NASA Astrophysics Data System (ADS)

Garkusha, A. V.; Kataev, A. L.; Molokoedov, V. S.

2018-02-01

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU( N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O({a}_s^4) level of perturbation theory. It is known that in the gauge-invariant renormalization \\overline{MS} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the \\overline{MS} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O({a}_s^3) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = -3 , -1 and ξ = 0. In the O({a}_s^4) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = -3 at the O({a}_s^3) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results

DOE PAGES

Nocera, Alberto; Wang, Yan; Patel, Niravkumar D.; ...

2018-05-31

Here, we study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gappedmore » spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.« less

Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals

DOE PAGES

Classen, Laura; Herbut, Igor F.; Scherer, Michael M.

2017-09-20

In this paper, we establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end, we study the quantum phase transition of gapless Dirac fermions coupled to a Z 3 symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model, the standard Landau-Ginzburg approach suggests a first-order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have tomore » be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions N f. A nonperturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers and we obtain the critical N f, where the nature of the transition changes. Furthermore, it is shown that for large N f the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. Finally, we compute the critical exponents and predict sizable corrections to scaling for N f = 2.« less

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nocera, Alberto; Wang, Yan; Patel, Niravkumar D.

Here, we study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gappedmore » spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehtola, Susi; Parkhill, John; Head-Gordon, Martin

Novel implementations based on dense tensor storage are presented here for the singlet-reference perfect quadruples (PQ) [J. A. Parkhill et al., J. Chem. Phys. 130, 084101 (2009)] and perfect hextuples (PH) [J. A. Parkhill and M. Head-Gordon, J. Chem. Phys. 133, 024103 (2010)] models. The methods are obtained as block decompositions of conventional coupled-cluster theory that are exact for four electrons in four orbitals (PQ) and six electrons in six orbitals (PH), but that can also be applied to much larger systems. PQ and PH have storage requirements that scale as the square, and as the cube of the numbermore » of active electrons, respectively, and exhibit quartic scaling of the computational effort for large systems. Applications of the new implementations are presented for full-valence calculations on linear polyenes (C nH n+2), which highlight the excellent computational scaling of the present implementations that can routinely handle active spaces of hundreds of electrons. The accuracy of the models is studied in the π space of the polyenes, in hydrogen chains (H 50), and in the π space of polyacene molecules. In all cases, the results compare favorably to density matrix renormalization group values. With the novel implementation of PQ, active spaces of 140 electrons in 140 orbitals can be solved in a matter of minutes on a single core workstation, and the relatively low polynomial scaling means that very large systems are also accessible using parallel computing.« less

Ground-state phase diagram of an anisotropic spin-1/2 model on the triangular lattice

NASA Astrophysics Data System (ADS)

Luo, Qiang; Hu, Shijie; Xi, Bin; Zhao, Jize; Wang, Xiaoqun

2017-04-01

Motivated by a recent experiment on the rare-earth material YbMgGaO4 [Y. Li et al., Phys. Rev. Lett. 115, 167203 (2015), 10.1103/PhysRevLett.115.167203], which found that the ground state of YbMgGaO4 is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-1 /2 model that was proposed to describe YbMgGaO4. Using the density matrix renormalization-group method in combination with the exact-diagonalization method, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram, there is a 120∘ phase and two distinct stripe phases. The transitions from the two stripe phases to the 120∘ phase are of the first order. However, the transition between the two stripe phases is not of the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may also be important to model the material YbMgGaO4. These findings will stimulate further experimental and theoretical works in understanding the quantum spin-liquid ground state in YbMgGaO4.

Higgs boson self-coupling from two-loop analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alhendi, H. A.; National Center for Mathematics and Physics, KACST P. O. Box 6086, Riyadh 11442; Barakat, T.

2010-09-01

The scale invariant of the effective potential of the standard model at two loop is used as a boundary condition under the assumption that the two-loop effective potential approximates the full effective potential. This condition leads with the help of the renormalization-group functions of the model at two loop to an algebraic equation of the scalar self-coupling with coefficients that depend on the gauge and the top quark couplings. It admits only two real positive solutions. One of them, in the absence of the gauge and top quark couplings, corresponds to the nonperturbative ultraviolet fixed point of the scalar renormalization-groupmore » function and the other corresponds to the perturbative infrared fixed point. The dependence of the scalar coupling on the top quark and the strong couplings at two-loop radiative corrections is analyzed.« less

Renormalization of the global quantum correlation and monogamy relation in the anisotropic Heisenberg XXZ model

NASA Astrophysics Data System (ADS)

Qin, Meng; Ren, Zhong-Zhou; Zhang, Xin

2016-01-01

In this study, the global quantum correlation, monogamy relation and quantum phase transition of the Heisenberg XXZ model are investigated by the method of quantum renormalization group. We obtain, analytically, the expressions of the global negativity, the global measurement-induced disturbance and the monogamy relation for the system. The result shows that for a three-site block state, the partial transpose of an asymmetric block can get stronger entanglement than that of the symmetric one. The residual entanglement and the difference of the monogamy relation of measurement-induced disturbance show a scaling behavior with the size of the system becoming large. Moreover, the monogamy nature of entanglement measured by negativity exists in the model, while the nonclassical correlation quantified by measurement-induced disturbance violates the monogamy relation and demonstrates polygamy.

Numerical Evidence for a Phase Transition in 4D Spin-Foam Quantum Gravity

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Steinhaus, Sebastian

2016-09-01

Building on recent advances in defining Wilsonian renormalization group (RG) flows, and the notion of scales in particular, for background-independent theories, we present a first investigation of the renormalization of the 4D spin-foam path integral for quantum gravity, both analytically and numerically. Focusing on a specific truncation of the model using a hypercubic lattice, we compute the RG flow and find strong indications for a phase transition, as well as an interesting interplay between the different observed phases and the (broken) diffeomorphism symmetry of the model. Most notably, it appears that the critical point between the phases, which is a fixed point of the RG flow, is precisely where broken diffeomorphism symmetry is restored, which suggests that it might allow us to define a continuum limit of the quantum gravity theory.

Numerical Evidence for a Phase Transition in 4D Spin-Foam Quantum Gravity.

PubMed

Bahr, Benjamin; Steinhaus, Sebastian

2016-09-30

Building on recent advances in defining Wilsonian renormalization group (RG) flows, and the notion of scales in particular, for background-independent theories, we present a first investigation of the renormalization of the 4D spin-foam path integral for quantum gravity, both analytically and numerically. Focusing on a specific truncation of the model using a hypercubic lattice, we compute the RG flow and find strong indications for a phase transition, as well as an interesting interplay between the different observed phases and the (broken) diffeomorphism symmetry of the model. Most notably, it appears that the critical point between the phases, which is a fixed point of the RG flow, is precisely where broken diffeomorphism symmetry is restored, which suggests that it might allow us to define a continuum limit of the quantum gravity theory.

Charged polymers in high dimensions

NASA Technical Reports Server (NTRS)

Kantor, Yacov

1990-01-01

A Monte Carlo study of charged polymers with either homogeneously distributed frozen charges or with mobile charges has been performed in four and five space dimensions. The results are consistent with the renormalization-group predictions and contradict the predictions of Flory-type theory. Introduction of charge mobility does not modify the behavior of the polymers.

Spin-adapted matrix product states and operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner–Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.

Recursive renormalization group theory based subgrid modeling

NASA Technical Reports Server (NTRS)

Zhou, YE

1991-01-01

Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.

Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaushal, Nitin; Herbrych, Jacek W.; Nocera, Alberto

Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t 2g) 4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard U and spin-orbit coupling λ, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase tomore » an excitonic insulator with increasing λ at intermediate U. In the strong U coupling limit, we find a nonmagnetic insulator with an effective angular momentum <(J eff) 2>≠0 near the excitonic phase, smoothly connected to the <(J eff) 2>=0 regime. In conclusion, we also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.« less

Renormalization-group flow of the effective action of cosmological large-scale structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Floerchinger, Stefan; Garny, Mathias; Tetradis, Nikolaos

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically,more » the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control.« less

Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension

NASA Astrophysics Data System (ADS)

Kaushal, Nitin; Herbrych, Jacek; Nocera, Alberto; Alvarez, Gonzalo; Moreo, Adriana; Reboredo, F. A.; Dagotto, Elbio

2017-10-01

Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t2g) 4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard U and spin-orbit coupling λ , at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing λ at intermediate U . In the strong U coupling limit, we find a nonmagnetic insulator with an effective angular momentum 〈(Jeff)2〉≠0 near the excitonic phase, smoothly connected to the 〈(Jeff)2〉=0 regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.

Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials.

PubMed

Wang, Jing

2018-03-28

We study the effects of four-fermion interaction and impurity on the low-energy states of 2D semi-Dirac materials by virtue of the unbiased renormalization group approach. The coupled flow equations that govern the energy-dependent evolutions of all correlated interaction parameters are derived after taking into account one-loop corrections from the interplay between four-fermion interaction and impurity. Whether and how four-fermion interaction and impurity influence the low-energy properties of 2D semi-Dirac materials are discreetly explored and addressed attentively. After carrying out the standard renormalization group analysis, we find that both trivial insulating and nontrivial semimetal states are qualitatively stable against all four kinds of four-fermion interactions. However, while switching on both four-fermion interaction and impurity, certain insulator-semimetal phase transitions and the distance of Dirac nodal points can be respectively induced and modified due to their strong interplay and intimate competition. Moreover, several non-Fermi liquid behaviors that deviate from the conventional Fermi liquids are exhibited at the lowest-energy limit.

Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension

DOE PAGES

Kaushal, Nitin; Herbrych, Jacek W.; Nocera, Alberto; ...

2017-10-09

Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t 2g) 4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard U and spin-orbit coupling λ, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase tomore » an excitonic insulator with increasing λ at intermediate U. In the strong U coupling limit, we find a nonmagnetic insulator with an effective angular momentum <(J eff) 2>≠0 near the excitonic phase, smoothly connected to the <(J eff) 2>=0 regime. In conclusion, we also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.« less

Density matrix renormalization group study of Y-junction spin systems

NASA Astrophysics Data System (ADS)

Guo, Haihui

Junction systems are important to understand both from the fundamental and the practical point of view, as they are essential components in existing and future electronic and spintronic devices. With the continuous advance of technology, device size will eventual reach the atomic scale. Some of the most interesting and useful junction systems will be strongly correlated. We chose the Density Matrix Renormalization Group method to study two types of Y-junction systems, the Y and YDelta junctions, on strongly correlated spin chains. With new ideas coming from the quantum information field, we have made a very efficient. Y-junction DMRG algorithm, which improves the overall CUB cost from O(m6) to O(m4), where m is the number of states kept per block. We studied the ground state properties, the correlation length, and investigated the degeneracy problem on the Y and YDelta junctions. For the excited states, we researched the existence of magnon bound states for various conditions, and have shown that the bound state exists when the central coupling constant is small.

Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity

NASA Astrophysics Data System (ADS)

Toniato, Júnior D.; Rodrigues, Davi C.; de Almeida, Álefe O. F.; Bertini, Nicolas

2017-09-01

We apply the full Will-Nordtvedt version of the parametrized post-Newtonian (PPN) formalism to a class of general relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant G is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the external potential effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales; for any of them the Solar System bounds need to be considered.

Renormalization group evolution of the universal theories EFT

DOE PAGES

Wells, James D.; Zhang, Zhengkang

2016-06-21

The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, butmore » dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. Finally, we perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.« less

Cook-Levin Theorem Algorithmic-Reducibility/Completeness = Wilson Renormalization-(Semi)-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') REPLACING CRUTCHES!!!: Models: Turing-machine, finite-state-models, finite-automata

NASA Astrophysics Data System (ADS)

Young, Frederic; Siegel, Edward

Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!

Unifying time evolution and optimization with matrix product states

NASA Astrophysics Data System (ADS)

Haegeman, Jutho; Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart; Verstraete, Frank

2016-10-01

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.

Backward renormalization-group inference of cortical dipole sources and neural connectivity efficacy

NASA Astrophysics Data System (ADS)

Amaral, Selene da Rocha; Baccalá, Luiz A.; Barbosa, Leonardo S.; Caticha, Nestor

2017-06-01

Proper neural connectivity inference has become essential for understanding cognitive processes associated with human brain function. Its efficacy is often hampered by the curse of dimensionality. In the electroencephalogram case, which is a noninvasive electrophysiological monitoring technique to record electrical activity of the brain, a possible way around this is to replace multichannel electrode information with dipole reconstructed data. We use a method based on maximum entropy and the renormalization group to infer the position of the sources, whose success hinges on transmitting information from low- to high-resolution representations of the cortex. The performance of this method compares favorably to other available source inference algorithms, which are ranked here in terms of their performance with respect to directed connectivity inference by using artificially generated dynamic data. We examine some representative scenarios comprising different numbers of dynamically connected dipoles over distinct cortical surface positions and under different sensor noise impairment levels. The overall conclusion is that inverse problem solutions do not affect the correct inference of the direction of the flow of information as long as the equivalent dipole sources are correctly found.