Theoretical investigation of the behavior of CuSe2O5 compound in high magnetic fields
NASA Astrophysics Data System (ADS)
Saghafi, Z.; Jahangiri, J.; Mahdavifar, S.; Hadipour, H.; Farjami Shayesteh, S.
2016-01-01
Based on the analytical and numerical approaches, we investigate thermodynamic properties of CuSe2O5 compound at high magnetic fields which is a candidate for the strong intra-chain interaction in quasi one-dimensional (1D) quantum magnets. Magnetic behavior of the system can be described by the 1D spin-1/2 XXZ model in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Under these circumstances, there is one quantum critical field in this compound. Below the quantum critical field the spin chain system is in the gapless Luttinger liquid (LL) regime, whereas above it one observes a crossover to the gapped saturation magnetic phase. Indications on the thermodynamic curves confirm the occurrence of such a phase transition. The main characteristics of the LL phase are gapless and spin-spin correlation functions decay algebraic. The effects of zero-temperature quantum phase transition are observed even at rather high temperatures in comparison with the counterpart compounds. In addition, we calculate the Wilson ratio in the model. The Wilson ratio at a fixed temperature remains almost independent of the field in the LL region. In the vicinity of the quantum critical field, the Wilson ratio increases and exhibits anomalous enhancement.
Thermodynamic properties of Heisenberg magnetic systems
NASA Astrophysics Data System (ADS)
Qin, Wei; Wang, Huai-Yu; Long, Gui-Lu
2014-03-01
In this paper, we present a comprehensive investigation of the effects of the transverse correlation function (TCF) on the thermodynamic properties of Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) systems with cubic lattices. The TCF of an FM system is positive and increases with temperature, while that of an AFM system is negative and decreases with temperature. The TCF lowers internal energy, entropy and specific heat. It always raises the free energy of an FM system but raises that of an AFM system only above a specific temperature when the spin quantum number is S >= 1. Comparisons between the effects of the TCFs on the FM and AFM systems are made where possible.
Chirality operators for Heisenberg spin systems
Subrahmanyam, V. )
1994-09-01
The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a twofold Kramers degeneracy. A nonzero chirality implies that the spins are not coplanar, and is a measure of handedness. The chirality operator, which can be treated as a spin-1/2 operator, is explicitly constructed in terms of the spin operators, and is given as commutator of permutation operators.
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu E-mail: zibo.miao@anu.edu.au; Miao, Zibo E-mail: zibo.miao@anu.edu.au; Amini, Hadis; Gough, John; Ugrinovskii, Valery; James, Matthew R.
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
NASA Astrophysics Data System (ADS)
Toranzo, I. V.; López-Rosa, S.; Esquivel, R. O.; Dehesa, J. S.
2015-06-01
Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for N -fermion d -dimensional systems. The contributions of both spatial and spin degrees of freedom are taken into account. The accuracy of some of these generalized spinned uncertainty-like relations is numerically examined for a large number of atomic and molecular systems.
Chiral-glass transition in a diluted dipolar-interaction Heisenberg system
NASA Astrophysics Data System (ADS)
Zhang, Kai-Cheng; Liu, Gui-Bin; Zhu, Yan
2011-05-01
Recently, numerical simulations reveal that a spin-glass transition can occur in the three-dimensional diluted dipolar system. By defining the chirality of triple spins in a diluted dipolar Heisenberg spin glass, we study the chiral ordering in the system using parallel tempering algorithm and heat bath method. The finite-size scaling analysis reveals that the system undergoes a chiral-glass transition at finite temperature.
Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems.
Ma, Xiao-song; Dakić, Borivoje; Kropatschek, Sebastian; Naylor, William; Chan, Yang-hao; Gong, Zhe-xuan; Duan, Lu-ming; Zeilinger, Anton; Walther, Philip
2014-01-01
Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.
NASA Astrophysics Data System (ADS)
Qin, Meng; Li, Yan-Biao; Wu, Fang-Ping
2014-07-01
Quantifying and understanding quantum correlations may give a direct reply for many issues regarding the interesting behaviors of quantum system. To explore the quantum correlations in quantum teleportation, we have used a two-qubit Heisenberg XYZ system with spin-orbit interaction as a quantum channel to teleport an unknown state. By using different measures and standard teleportation protocols, we have derived the analytical expressions for quantum discord, entanglement of formation, purity, and maximal teleportation fidelity of the system. We compare their different characteristics and analyze the relationships between these quantities.
Heisenberg-like uncertainty measures for D-dimensional hydrogenic systems at large D
NASA Astrophysics Data System (ADS)
Toranzo, I. V.; Martínez-Finkelshtein, A.; Dehesa, J. S.
2016-08-01
The radial expectation values of the probability density of a quantum system in position and momentum spaces allow one to describe numerous physical quantities of the system as well as to find generalized Heisenberg-like uncertainty relations and to bound entropic uncertainty measures. It is known that the position and momentum expectation values of the main prototype of the D-dimensional Coulomb systems, the D-dimensional hydrogenic system, can be expressed in terms of some generalized hypergeometric functions of the type p+1Fp(z) evaluated at unity with p = 2 and p = 3, respectively. In this work we determine the position and momentum expectation values in the limit of large D for all hydrogenic states from ground to very excited (Rydberg) ones in terms of the spatial dimensionality and the hyperquantum numbers of the state under consideration. This is done by means of two different approaches to calculate the leading term of the special functions 3 F 2 (" separators=" 1 ) and 5 F 4 (" separators=" 1 ) involved in the large D limit of the position and momentum quantities. Then, these quantities are used to obtain the generalized Heisenberg-like and logarithmic uncertainty relations, and some upper and lower bounds to the entropic uncertainty measures (Shannon, Rényi, Tsallis) of the D-dimensional hydrogenic system.
Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
NASA Astrophysics Data System (ADS)
Derzhko, Oleg; Richter, Johannes; Maksymenko, Mykola
2015-05-01
On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli
Entanglement in a four qubit J1-J2 Heisenberg XXZ system with Dzialoshinskii-Moriya interaction
NASA Astrophysics Data System (ADS)
Şahintaş, Alev; Akyüz, Cenk
2016-04-01
In this study, we investigate the entanglement properties of a four qubit anisotropic Heisenberg XXZ system which has the nearest neighboring (NN), the next nearest neighboring (NNN) and Dzialoshinskii-Moriya (DM) interactions. Calculations of the ground state and thermal entanglement are carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, anisotropy and frustration. From the results obtained, we see that DM interaction and the frustration play an active role on the ground state entanglement between NN and NNN qubits, respectively. We also see that frustration parameter α exhibits positive effects on the thermal entanglement especially between NNN qubits. Consequently, we show that effective control of entanglement can be obtained by employing competing effects of the control parameters in this general Heisenberg model which is constructed by considering not only NN interaction but also NNN and DM interactions.
1 /f α noise and generalized diffusion in random Heisenberg spin systems
NASA Astrophysics Data System (ADS)
Agarwal, Kartiek; Demler, Eugene; Martin, Ivar
2015-11-01
We study the "flux-noise" spectrum of random-bond quantum Heisenberg spin systems using a real-space renormalization group (RSRG) procedure that accounts for both the renormalization of the system Hamiltonian and of a generic probe that measures the noise. For spin chains, we find that the dynamical structure factor Sq(f ) , at finite wave vector q , exhibits a power-law behavior both at high and low frequencies f , with exponents that are connected to one another and to an anomalous dynamical exponent through relations that differ at T =0 and T =∞ . The low-frequency power-law behavior of the structure factor is inherited by any generic probe with a finite bandwidth and is of the form 1 /fα with 0.5 <α <1 . An analytical calculation of the structure factor, assuming a limiting distribution of the RG flow parameters (spin size, length, bond strength) confirms numerical findings. More generally, we demonstrate that this form of the structure factor, at high temperatures, is a manifestation of anomalous diffusion which directly follows from a generalized spin-diffusion propagator. We also argue that 1 /f -noise is intimately connected to many-body-localization at finite temperatures. In two dimensions, the RG procedure is less reliable; however, it becomes convergent for quasi-one-dimensional geometries where we find that one-dimensional 1 /fα behavior is recovered at low frequencies; the latter configurations are likely representative of paramagnetic spin networks that produce 1 /fα noise in SQUIDs.
Berry phase in Heisenberg representation
NASA Technical Reports Server (NTRS)
Andreev, V. A.; Klimov, Andrei B.; Lerner, Peter B.
1994-01-01
We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.
Influence of the nonmagnetic impurities on the spin-1 Heisenberg chain SrNi2V2O8 system
NASA Astrophysics Data System (ADS)
Giapintzakis, J.; Androulakis, J.; Syskakis, E.; Papageorgiou, Th. P.; Apostolopoulos, G.; Thanos, S.; Papastaikoudis, C.
Dc-magnetization and heat capacity measurements on polycrystalline samples of SrNi2-x Mgx V2O8 (x = 0 and 0.05) are reported. The magnetization data suggest that both compounds are S = 1 quasi one-dimensional Heisenberg antiferromagnets. The substitution of non-magnetic impurity Mg2+ ions for Ni2+ induces a magnetic phase transition at ?3.7 K. A simple Hamiltonian model is proposed for these systems giving good quantitative agreement with the experimental magnetization data. The intrachain magnetic exchange constant (J 1/k B) and the Haldane gap (? ) for both compounds are estimated to be ?105 K and ?58.3 K (5.02 meV), respectively.
ERIC Educational Resources Information Center
Cassidy, David C.
1978-01-01
Describes some of the discussion, correspondances and assumptions of Heisenberg. Includes clarifying and defending his explanation of the anomalous Zeeman Effect to the Quantum Physicists of his time. (GA)
Heisenberg's observability principle
NASA Astrophysics Data System (ADS)
Wolff, Johanna
2014-02-01
Werner Heisenberg's 1925 paper 'Quantum-theoretical re-interpretation of kinematic and mechanical relations' marks the beginning of quantum mechanics. Heisenberg famously claims that the paper is based on the idea that the new quantum mechanics should be 'founded exclusively upon relationships between quantities which in principle are observable'. My paper is an attempt to understand this observability principle, and to see whether its employment is philosophically defensible. Against interpretations of 'observability' along empiricist or positivist lines I argue that such readings are philosophically unsatisfying. Moreover, a careful comparison of Heisenberg's reinterpretation of classical kinematics with Einstein's argument against absolute simultaneity reveals that the positivist reading does not fit with Heisenberg's strategy in the paper. Instead the appeal to observability should be understood as a specific criticism of the causal inefficacy of orbital electron motion in Bohr's atomic model. I conclude that the tacit philosophical principle behind Heisenberg's argument is not a positivistic connection between observability and meaning, but the idea that a theory should not contain causally idle wheels.
Phase Separation in the Heisenberg Spin System, Gd2Ti2O7
NASA Astrophysics Data System (ADS)
Gardner, J. S.; Stewart, J. R.; Ehlers, G.
2010-01-01
Gd2Ti2O7 is a geometrically frustrated antiferromagnetic system with two magnetic phase transitions at 1.1 K and 0.7 K. The determination of the magnetic structure in the ordered phases by a powder measurement is greatly complicated by the ambiguity between 1-k and 4-k structures resulting in identical structure factors. Here we will present data and new analyses showing that, as the system cools from the correlated, paramagnetic regime just above 1 K, (i) the magnetic system freezes into a partially ordered state, and (ii) the 4-k structure is maintained throughout down to a base temperature <50 mK. This clears up the ambiguity in the magnetic structure and confirms the phase separation of the Gd-sites into two in equivalent sites with a 3:1 ratio.
Theory of disordered Heisenberg ferromagnets
NASA Technical Reports Server (NTRS)
Stubbs, R. M.
1973-01-01
A Green's function technique is used to calculate the magnetic properties of Heisenberg ferromagnets in which the exchange interactions deviate randomly in strength from the mean interaction. Systems of sc, bcc, and fcc topologies and of general spin values are treated. Disorder produces marked effects in the density of spin wave states, in the form of enhancement of the low-energy density and extension of the energy band to higher values. The spontaneous magnetization and the Curie temperature decrease with increasing disorder. The effects of disorder are shown to be more pronounced in the ferromagnetic than in the paramagnetic phase.
Integrable hierarchies of Heisenberg ferromagnet equation
NASA Astrophysics Data System (ADS)
Nugmanova, G.; Azimkhanova, A.
2016-08-01
In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.
Fourier optics from the perspective of the Heisenberg group
NASA Astrophysics Data System (ADS)
Raszillier, Hans; Schempp, Walter
Introduction The quantization problem The Heisenberg group Description of the wave field Examples from quantum mechanics The phase space of geometrical optics Peculiarities of geometrical optics Phase discontinuities Systems with symmetry Summary and comments References
Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
NASA Astrophysics Data System (ADS)
Vinet, Luc; Zhedanov, Alexei
2008-02-01
We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution) interpretation of the corresponding integrable systems.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2009-02-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2011-09-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
Sub-Heisenberg phase uncertainties
NASA Astrophysics Data System (ADS)
Pezzé, Luca
2013-12-01
Phase shift estimation with uncertainty below the Heisenberg limit, ΔϕHL∝1/N¯T, where N¯T is the total average number of particles employed, is a mirage of linear quantum interferometry. Recently, Rivas and Luis, [New J. Phys.NJOPFM1367-263010.1088/1367-2630/14/9/093052 14, 093052 (2012)] proposed a scheme to achieve a phase uncertainty Δϕ∝1/N¯Tk, with k an arbitrary exponent. This sparked an intense debate in the literature which, ultimately, does not exclude the possibility to overcome ΔϕHL at specific phase values. Our numerical analysis of the Rivas and Luis proposal shows that sub-Heisenberg uncertainties are obtained only when the estimator is strongly biased. No violation of the Heisenberg limit is found after bias correction or when using a bias-free Bayesian analysis.
Heisenberg and the critical mass
NASA Astrophysics Data System (ADS)
Bernstein, Jeremy
2002-09-01
An elementary treatment of the critical mass used in nuclear weapons is presented and applied to an analysis of the wartime activities of the German nuclear program. In particular, the work of Werner Heisenberg based on both wartime and postwar documents is discussed.
NASA Astrophysics Data System (ADS)
Yersultanova, Z. S.; Zhassybayeva, M.; Yesmakhanova, K.; Nugmanova, G.; Myrzakulov, R.
2016-10-01
Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.
Integrable higher order deformations of Heisenberg supermagnetic model
Guo Jiafeng; Yan Zhaowen; Wang Shikun; Wu Ke; Zhao Weizhong
2009-11-15
The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S{sup 2}=3S-2I for S is an element of USPL(2/1)/S(U(2)xU(1)) and (ii) S{sup 2}=S for S is an element of USPL(2/1)/S(L(1/1)xU(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.
Conjugacy classes in discrete Heisenberg groups
Budylin, R Ya
2014-08-01
We study an extension of a discrete Heisenberg group coming from the theory of loop groups and find invariants of conjugacy classes in this group. In some cases, including the case of the integer Heisenberg group, we make these invariants more explicit. Bibliography: 4 titles.
Did Heisenberg Spit at Max Born?
NASA Astrophysics Data System (ADS)
Lustig, Harry
2005-04-01
In his 1985 book ``The Griffin,'' Arnold Kramish quotes an unnamed ``associate'' of Max Born that when Heisenberg ''was . . . a professor in Göttingen and when the Borns went to visit him, they were met with anti-Jewish sneers and obscenities, and in the end Heisenberg spat on the floor at Max Born's feet!". Kramish, in his own words, states that Heisenberg spat at Born and that the incident took place in 1933. Paul Lawrence Rose places the incident in 1953 and, on the basis of a fuller account from Kramish than the one published, identifies the associate as Born's secretary at Edinburgh University. One may be critical of Heisenberg's character and his behavior under the Nazis, and still be highly skeptical of the Kramish-Rose allegation. The life-long friendship between Born and Heisenberg and the respect which they displayed for each other before, during, and after the Nazi regime, has hardly been challenged by anyone. No known biography of Heisenberg mentions the alleged episode, and none of his obituaries alludes to it. There is no reference to it in Born's autobiography. None of the historians of science, German and American, whom I have consulted credit it. Although it is difficult to prove a negative, it is highly unlikely that Heisenberg spit at Born or on the floor on which they stood.
NASA Astrophysics Data System (ADS)
Yang, Chen Ning
2013-05-01
Werner Heisenberg was one of the greatest physicists of all times. When he started out as a young research worker, the world of physics was in a very confused and frustrating state, which Abraham Pais has described1 as: It was the spring of hope, it was the winter of despair using Charles Dickens' words in A Tale of Two Cities. People were playing a guessing game: There were from time to time great triumphs in proposing, through sheer intuition, make-shift schemes that amazingly explained some regularities in spectral physics, leading to joy. But invariably such successes would be followed by further work which reveal the inconsistency or inadequacy of the new scheme, leading to despair...
Far-from-equilibrium spin transport in Heisenberg quantum magnets.
Hild, Sebastian; Fukuhara, Takeshi; Schauß, Peter; Zeiher, Johannes; Knap, Michael; Demler, Eugene; Bloch, Immanuel; Gross, Christian
2014-10-01
We study experimentally the far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice. After controlled imprinting of a spin spiral pattern with an adjustable wave vector, we measure the decay of the initial spin correlations through single-site resolved detection. On the experimentally accessible time scale of several exchange times, we find a profound dependence of the decay rate on the wave vector. In one-dimensional systems, we observe diffusionlike spin transport with a dimensionless diffusion coefficient of 0.22(1). We show how this behavior emerges from the microscopic properties of the closed quantum system. In contrast to the one-dimensional case, our transport measurements for two-dimensional Heisenberg systems indicate anomalous superdiffusion. PMID:25325657
Quantum states for Heisenberg-limited interferometry
Uys, H.; Meystre, P.
2007-07-15
The phase sensitivity of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N, a 1/{radical}(N) improvement over the standard quantum limit. We have used simulated annealing, a global optimization strategy, to systematically search for quantum interferometer input states that approach the Heisenberg-limited uncertainty in estimates of the interferometer phase shift. We compare the performance of these states to that of other nonclassical states already known to yield Heisenberg-limited uncertainty.
100 Years Werner Heisenberg: Works and Impact
NASA Astrophysics Data System (ADS)
Papenfuß, Dietrich; Lüst, Dieter; Schleich, Wolfgang P.
2003-09-01
Over 40 renowned scientists from all around the world discuss the work and influence of Werner Heisenberg. The papers result from the symposium held by the Alexander von Humboldt-Stiftung on the occasion of the 100th anniversary of Heisenberg's birth, one of the most important physicists of the 20th century and cofounder of modern-day quantum mechanics. Taking atomic and laser physics as their starting point, the scientists illustrate the impact of Heisenberg's theories on astroparticle physics, high-energy physics and string theory right up to processing quantum information.
Adiabatic limits on Riemannian Heisenberg manifolds
Yakovlev, A A
2008-02-28
An asymptotic formula is obtained for the distribution function of the spectrum of the Laplace operator, in the adiabatic limit for the foliation defined by the orbits of an invariant flow on a compact Riemannian Heisenberg manifold. Bibliography: 21 titles.
Decay of transverse correlations in quantum Heisenberg models
Björnberg, Jakob E. E-mail: daniel@ueltschi.org; Ueltschi, Daniel E-mail: daniel@ueltschi.org
2015-04-15
We study a class of quantum spin systems that include the S=1/2 Heisenberg and XY-models and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random loop representations of the correlation functions, on stochastic domination and on first-passage percolation.
The role of phase space geometry in Heisenberg's uncertainty relation
NASA Astrophysics Data System (ADS)
Anastopoulos, Charis; Savvidou, Ntina
2003-11-01
Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the time-energy ones). The metric also distinguishes the original uncertainty relations of Heisenberg from the ones that are obtained from non-commutativity of operators. Conversely, the uncertainty relations can be written in terms of this metric only, hence they can be formulated for any physical system, including ones with non-trivial phase space. Moreover, the metric is a key ingredient of the probability structure of continuous-time histories on phase space. This fact allows a simple new proof the impossibility of the physical manifestation of the quantum Zeno and anti-Zeno paradoxes. Finally, we construct the coherent states for a spinless relativistic particle, as a non-trivial example by which we demonstrate our results.
Open timelike curves violate Heisenberg's uncertainty principle.
Pienaar, J L; Ralph, T C; Myers, C R
2013-02-01
Toy models for quantum evolution in the presence of closed timelike curves have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require nontrivial interactions between the future and past that lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the closed timelike curve, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time dilation suggests that OTCs provide a novel alternative to existing proposals for the behavior of quantum systems under gravity.
Quantification of quantum discord in a antiferromagnetic Heisenberg compound
Singh, H. Chakraborty, T. Mitra, C.
2014-04-24
An experimental quantification of concurrence and quantum discord from heat capacity (C{sub p}) measurement performed over a solid state system has been reported. In this work, thermodynamic measurements were performed on copper nitrate (CN, Cu(NO{sub 3}){sub 2}⋅2.5H{sub 2}O) single crystals which is an alternating antiferromagnet Heisenberg spin 1/2 system. CN being a weak dimerized antiferromagnet is an ideal system to investigate correlations between spins. The theoretical expressions were used to obtain concurrence and quantum discord curves as a function of temperature from heat capacity data of a real macroscopic system, CN.
Nonlinear phonon interferometry at the Heisenberg limit
NASA Astrophysics Data System (ADS)
Cheung, Hil F. H.; Patil, Yogesh Sharad; Chang, Laura; Chakram, Srivatsan; Vengalattore, Mukund
2016-05-01
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ 1 /√{ N}) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. Here, we realize a prominent example of such schemes, the so-called SU(1,1) interferometer, in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ 1 / N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. We describe how our work extends the optomechanical toolbox and how it presents new avenues for studies of optomechanical sensing and studies of nonequilibrium dynamics of multimode optomechanical systems. This work was supported by the DARPA QuASAR program through a grant from the ARO, the ARO MURI on non-equilibrium manybody dynamics and an NSF INSPIRE award.
Heisenberg: Paralleling Scientific and Historical Methods
NASA Astrophysics Data System (ADS)
Cofield, Calla
2007-04-01
Werner Heisenberg is an important historical subject within the physics community partly because his actions as a human being are discussed nearly as often as his work as a physicist. But does the scientific community establish it's historical ideas with the same methods and standards as it's scientific conclusions? I interviewed Heisenberg's son, Jochen Heisenberg, a professor of physics at UNH. Despite a great amount of literature on Werner Heisenberg, only one historian has interviewed Jochen about his father and few have interviewed Werner's wife. Nature is mysterious and unpredictable, but it doesn't lie or distort like humans, and we believe it can give ``honest'' results. But are we keeping the same standards with history that we do with science? Are we holding historians to these standards and if not, is it up to scientists to not only be keepers of scientific understanding, but historical understanding as well? Shouldn't we record history by using the scientific method, by weighing the best sources of data differently than the less reliable, and are we right to be as stubborn about changing our views on history as we are about changing our views on nature?
Naturalistic Misunderstanding of the Heisenberg Uncertainty Principle.
ERIC Educational Resources Information Center
McKerrow, K. Kelly; McKerrow, Joan E.
1991-01-01
The Heisenberg Uncertainty Principle, which concerns the effect of observation upon what is observed, is proper to the field of quantum physics, but has been mistakenly adopted and wrongly applied in the realm of naturalistic observation. Discusses the misuse of the principle in the current literature on naturalistic research. (DM)
Phase diagrams of the Ising-Heisenberg chain with S = 1/2 triangular XXZ clusters
Ohanyan, V.
2010-03-15
The one-dimensional spin system consisted of triangular S = 1/2 XXZ Heisenberg clusters alternating with single Ising spins is considered. Partition function of the system is calculated exactly within the transfer-matrix formalism. T = 0 ground state phase diagrams, corresponding to different regions of the values of system parameters, are obtained.
Heisenberg necklace model in a magnetic field
NASA Astrophysics Data System (ADS)
Tsvelik, A. M.; Zaliznyak, I. A.
2016-08-01
We study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J . We consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I =3 /2 ) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ ˜J1 /3(γI ) 2 /3 , at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. This energy scale is insensitive to a magnetic field B . For μBB >Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, √{2 }+1 .
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
Frustrated 3×3 Heisenberg antiferromagnets
NASA Astrophysics Data System (ADS)
Moustanis, P. N.
2016-08-01
The full energy spectrum and the exact thermodynamic results of the antiferromagnetic Heisenberg Hamiltonian of the 3×3 triangular and the frustrated square lattice with periodic boundary conditions and s=1/2 are obtained. To this end the method of hierarchy of algebras is employed. It was found that the ground state of the 3×3 frustrated square lattice is a Resonating Valence Bond (RVB) state. Thermodynamic properties, like the specific heat, magnetic susceptibility, the thermal average of the square of the total Sz and entropy, for these two lattices are presented.
Heisenberg scaling in Gaussian quantum metrology
NASA Astrophysics Data System (ADS)
Friis, Nicolai; Skotiniotis, Michalis; Fuentes, Ivette; Dür, Wolfgang
2015-08-01
We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field. Such Bogoliubov transformations frequently appear in the context of quantum optics. We provide a set of instructions for computing the quantum Fisher information for arbitrary pure initial states. We show that the maximally achievable precision of estimation is inversely proportional to the squared average particle number and that such Heisenberg scaling requires nonclassical but not necessarily entangled states. Our method further allows us to quantify losses in precision arising from being able to monitor only finitely many modes, for which we identify a lower bound.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
q-bosons and the Lie-deformed Heisenberg algebra
NASA Astrophysics Data System (ADS)
Pan, Hui-yun; Zhao, Zu Sen
1998-02-01
It is shown that the non-Hermitian realization of a Lie-deformed Heisenberg algebra given by Jannussis et al. is closely related with the q-Heisenberg-Weyl algebra of Biedenharn and Macfarlane with q being a phase ( q = eiθ, with θ real). The physical implications of this result are stressed.
Science 101: What, Exactly, Is the Heisenberg Uncertainty Principle?
ERIC Educational Resources Information Center
Robertson, Bill
2016-01-01
Bill Robertson is the author of the NSTA Press book series, "Stop Faking It! Finally Understanding Science So You Can Teach It." In this month's issue, Robertson describes and explains the Heisenberg Uncertainty Principle. The Heisenberg Uncertainty Principle was discussed on "The Big Bang Theory," the lead character in…
Quantum spin transistor with a Heisenberg spin chain
NASA Astrophysics Data System (ADS)
Marchukov, O. V.; Volosniev, A. G.; Valiente, M.; Petrosyan, D.; Zinner, N. T.
2016-10-01
Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements.
Quantum spin transistor with a Heisenberg spin chain
Marchukov, O. V.; Volosniev, A. G.; Valiente, M.; Petrosyan, D.; Zinner, N. T.
2016-01-01
Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements. PMID:27721438
Fractionalized Fermi liquid in a Kondo-Heisenberg model
NASA Astrophysics Data System (ADS)
Tsvelik, A. M.
2016-10-01
The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. In agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003), 10.1103/PhysRevLett.90.216403], the resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations. The system undergoes a phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.
Correlation length of the isotropic quantum Heisenberg antiferromagnet
Cuccoli, A.; Tognetti, V.; Vaia, R.
1997-04-01
The quantum Heisenberg antiferromagnet on the square lattice is known to model the magnetic interactions in the copper ion planes of many high-{ital T{sub c}} superconductors and their parent compounds. The thermodynamics of the model is approached by the {ital pure-quantum self-consistent harmonic approximation}, that reduces the quantum problem to the study of an effective classical antiferromagnetic system. The effective exchange, weakened by quantum fluctuations, enters as a temperature scale the classical-like expressions for the thermal averages, and the quantum spin correlation length is then obtained from its classical counterpart in a simple way. The theory compares very well, for any value of the spin and without need for adjustable parameters, with high temperature expansions, quantum Monte Carlo simulations, and recent neutron and nuclear quadrupole relaxation (NQR) experiments. {copyright} {ital 1997 American Institute of Physics.}
Two Spin Liquid phases in the anisotropic triangular Heisenberg model
NASA Astrophysics Data System (ADS)
Sorella, Sandro
2005-03-01
Recently there have been rather clean experimental realizations of the quantum spin 1/2 Heisenberg Hamiltonian on a 2D triangular lattice geometry in systems like Cs2Cu Cl4 and organic compounds like k-(ET)2Cu2(CN)3. These materials are nearly two dimensional and are characterized by an anisotropic antiferromagnetic superexchange. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to non conventional spin liquid phases. In order to understand these interesting phenomena we have studied, by Quantum Monte Carlo methods, the triangular lattice Heisenberg model as a function of the strength of this anisotropy, represented by the ratio r between the intra-chain nearest neighbor coupling J' and the inter-chain one J. We have found evidence of two spin liquid regions, well represented by projected BCS wave functions[1,2] of the type proposed by P. W. Anderson at the early stages of High temperature superconductivity [3]. The first spin liquid phase is stable for small values of the coupling r 0.6 and appears gapless and fractionalized, whereas the second one is a more conventional spin liquid, very similar to the one realized in the quantum dimer model in the triangular lattice[4]. It is characterized by a spin gap and a finite correlation length, and appears energetically favored in the region 0.6 r 0.9. The various phases are in good agreement with the experimental findings and supports the existence of spin liquid phases in 2D quantum spin-half systems. %%%%%%%%%%%%%%%%%% 1cm *[1] L. Capriotti F. Becca A. Parola and S. Sorella , Phys. Rev. Letters 87, 097201 (2001). *[2] S. Yunoki and S. Sorella Phys. Rev. Letters 92, 15003 (2004). *[3] P. W. Anderson, Science 235, 1186 (1987). *[4] P. Fendley, R. Moessner, and S. L. Sondhi Phys. Rev. B 66, 214513 (2002).
Unified molecular field theory for collinear and noncollinear Heisenberg antiferromagnets
Johnston, David C.
2015-02-27
In this study, a unified molecular field theory (MFT) is presented that applies to both collinear and planar noncollinear Heisenberg antiferromagnets (AFs) on the same footing. The spins in the system are assumed to be identical and crystallographically equivalent. This formulation allows calculations of the anisotropic magnetic susceptibility χ versus temperature T below the AF ordering temperature T_{N} to be carried out for arbitrary Heisenberg exchange interactions J_{ij} between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature θ_{p} in the Curie-Weiss law is written in terms of the J_{ij} values and T_{N} in terms of the J_{ij} values and an assumed AF structure. Other magnetic and thermal properties are then expressed in terms of quantities easily accessible from experiment as laws of corresponding states for a given spin S. For collinear ordering these properties are the reduced temperature t=T/T_{N}, the ratio f = θ_{p}/T_{N}, and S. For planar noncollinear helical or cycloidal ordering, an additional parameter is the wave vector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that χ(T ≤ T_{N}) of noncollinear 120° spin structures on triangular lattices is isotropic and independent of S and T and thus clarifies the origin of this universally observed behavior. The high-field magnetization and heat capacity for fields applied perpendicular to the ordering axis (collinear AFs) and ordering plane (planar noncollinear AFs) are also calculated and expressed for both types of AF structures as laws of corresponding states for a given S, and the reduced perpendicular field versus reduced temperature phase diagram is constructed.
Unified molecular field theory for collinear and noncollinear Heisenberg antiferromagnets
Johnston, David C.
2015-02-27
In this study, a unified molecular field theory (MFT) is presented that applies to both collinear and planar noncollinear Heisenberg antiferromagnets (AFs) on the same footing. The spins in the system are assumed to be identical and crystallographically equivalent. This formulation allows calculations of the anisotropic magnetic susceptibility χ versus temperature T below the AF ordering temperature TN to be carried out for arbitrary Heisenberg exchange interactions Jij between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature θp in the Curie-Weiss law is written in terms of the Jij values and TNmore » in terms of the Jij values and an assumed AF structure. Other magnetic and thermal properties are then expressed in terms of quantities easily accessible from experiment as laws of corresponding states for a given spin S. For collinear ordering these properties are the reduced temperature t=T/TN, the ratio f = θp/TN, and S. For planar noncollinear helical or cycloidal ordering, an additional parameter is the wave vector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that χ(T ≤ TN) of noncollinear 120° spin structures on triangular lattices is isotropic and independent of S and T and thus clarifies the origin of this universally observed behavior. The high-field magnetization and heat capacity for fields applied perpendicular to the ordering axis (collinear AFs) and ordering plane (planar noncollinear AFs) are also calculated and expressed for both types of AF structures as laws of corresponding states for a given S, and the reduced perpendicular field versus reduced temperature phase diagram is constructed.« less
Unified molecular field theory for collinear and noncollinear Heisenberg antiferromagnets
NASA Astrophysics Data System (ADS)
Johnston, David C.
2015-02-01
A unified molecular field theory (MFT) is presented that applies to both collinear and planar noncollinear Heisenberg antiferromagnets (AFs) on the same footing. The spins in the system are assumed to be identical and crystallographically equivalent. This formulation allows calculations of the anisotropic magnetic susceptibility χ versus temperature T below the AF ordering temperature TN to be carried out for arbitrary Heisenberg exchange interactions Ji j between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature θp in the Curie-Weiss law is written in terms of the Ji j values and TN in terms of the Ji j values and an assumed AF structure. Other magnetic and thermal properties are then expressed in terms of quantities easily accessible from experiment as laws of corresponding states for a given spin S . For collinear ordering these properties are the reduced temperature t =T /TN , the ratio f =θp/TN , and S . For planar noncollinear helical or cycloidal ordering, an additional parameter is the wave vector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that χ (T ≤TN) of noncollinear 120∘ spin structures on triangular lattices is isotropic and independent of S and T and thus clarifies the origin of this universally observed behavior. The high-field magnetization and heat capacity for fields applied perpendicular to the ordering axis (collinear AFs) and ordering plane (planar noncollinear AFs) are also calculated and expressed for both types of AF structures as laws of corresponding states for a given S , and the reduced perpendicular field versus reduced temperature phase diagram is constructed.
An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains
NASA Astrophysics Data System (ADS)
Joel, Kira; Kollmar, Davida; Santos, Lea F.
2013-06-01
Quantum spin chains are prototype quantum many-body systems that are employed in the description of various complex physical phenomena. We provide an introduction to this subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.
Heisenberg-Weyl Observables: Bloch vectors in phase space
NASA Astrophysics Data System (ADS)
Asadian, Ali; Erker, Paul; Huber, Marcus; Klöckl, Claude
2016-07-01
We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anticommuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first nontrivial example beyond the dichotomic case.
NASA Astrophysics Data System (ADS)
Alécio, Raphael C.; Lyra, Marcelo L.; Strečka, Jozef
2016-11-01
The ground-state phase diagram, magnetization process and bipartite entanglement of the frustrated spin-1/2 Ising-Heisenberg and Heisenberg triangular tube (three-leg ladder) are investigated in a non-zero external magnetic field. The exact ground-state phase diagram of the spin-1/2 Ising-Heisenberg tube with Heisenberg intra-rung and Ising inter-rung couplings consists of six distinct gapped phases, which manifest themselves in a magnetization curve as intermediate plateaus at zero, one-third and two-thirds of the saturation magnetization. Four out of six available ground states exhibit quantum entanglement between two spins from the same triangular unit evidenced by a non-zero concurrence. Density-matrix renormalization group calculations are used in order to construct the ground-state phase diagram of the analogous but purely quantum spin-1/2 Heisenberg tube with Heisenberg intra- and inter-rung couplings, which consists of four gapped and three gapless phases. The Heisenberg tube shows a continuous change of the magnetization instead of a plateau at zero magnetization, while the intermediate one-third and two-thirds plateaus may be present or not in the zero-temperature magnetization curve.
Aharonov-Bohm effect in quantum-to-classical correspondence of the Heisenberg principle
Lin, D.-H.; Chang, J.-G.; Hwang, C.-C.
2003-04-01
The exact energy spectrum and wave function of a charged particle moving in the Coulomb field and Aharonov-Bohm's magnetic flux are solved by the nonintegrable phase factor. The universal formula for the matrix elements of the radial operator r{sup {alpha}} of arbitrary power {alpha} is given by an analytical solution. The difference between the classical limit of matrix elements of inverse radius in quantum mechanics and the Fourier components of the corresponding quantity for the pure Coulomb system in classical mechanics is examined in reference to the correspondence principle of Heisenberg. Explicit calculation shows that the influence of nonlocal Aharonov-Bohm effect exists even in the classical limit. The semiclassical quantization rule for systems containing the topological effect is presented in the light of Heisenberg's corresponding principle.
Whittaker modules for the twisted Heisenberg-Virasoro algebra
Liu Dong; Wu Yuezhu; Zhu Linsheng
2010-02-15
We define Whittaker modules for the twisted Heisenberg-Virasoro algebra and obtain several results from the classical setting, including a classification of simple Whittaker modules by central characters.
Heisenberg's Uncertainty Principle and Interpretive Research in Science Education.
ERIC Educational Resources Information Center
Roth, Wolff-Michael
1993-01-01
Heisenberg's uncertainty principle and the derivative notions of interdeterminacy, uncertainty, precision, and observer-observed interaction are discussed and their applications to social science research examined. Implications are drawn for research in science education. (PR)
Stable mean-field solution of a short-range interacting SO(3) quantum Heisenberg spin glass.
da Conceição, C M S; Marino, E C
2008-07-18
We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an antiferromagnetic (AF) coupling J[over ]>0, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a Néel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.
Heisenberg Groups and their Automorphisms over Algebras with Central Involution
NASA Astrophysics Data System (ADS)
Johnson, Robert W.
2015-08-01
Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real and complex quadratic spaces with dimension 4 or less. A model for the representations of these Heisenberg groups and automorphism groups is constructed. A pseudo-differential operator enables a parallel treatment of spaces defined over finite and real fields.
Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet
Fu, Mingxuan; Imai, Takahashi; Han, Tian -Heng; Lee, Young S.
2015-11-06
Here, the kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χkagome, deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with themore » magnetic field dependence of χkagome that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.« less
Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet.
Fu, Mingxuan; Imai, Takashi; Han, Tian-Heng; Lee, Young S
2015-11-01
The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χ(kagome), deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with the magnetic field dependence of χ(kagome) that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap. PMID:26542565
High Field Magnetization Studies of Low Dimensional Heisenberg S = 1/2 Antiferromagnets
NASA Astrophysics Data System (ADS)
Landee, C. P.; Albrecht, A. S.; Turnbull, M. M.
1997-03-01
The magnetization curves of a number of new 2D S=1/2 Heisenberg antiferromagnets have been determined in fields up to 30 tesla at low temperatures at the National High Magnetic Fields Laboratory. Magnets studied include (2-amino-5-methylpyridinium)_2CuBr4 (2-amino-5-chloropyridinium)_2CuBr_4, and [Cu(pz)_2(NO_3)](PF_6), where pz = pyrazine. All of the magnetization curves show upward curvature, a previously unknown effect for this model system. The magnetization curves are qualitatively similar to the theoretical prediction for the linear chain Heisenberg antiferromagnet. The saturation fields are consistent with those predicted from a molecular-field model, using exchange strengths obtained from susceptibility studies. Slight anisotropy has been observed in the single crystal studies of (2-amino-5-methylpyridinium)_2CuBr_4.
Shuaibu, A.; Rahman, M. M.
2014-03-05
We study the low temperature behavior of a triangular lattice quantum spin-1 Heisenberg antiferromagnet with single-site anisotropy by using coordinate Bethe ansatz method. We compute the standard two-particle Hermitian Hamiltonian, and obtain the eigenfunctions and eigenvalue of the system. The obtained results show a number of advantages in comparison with many results.
Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.
Kvashnin, Y O; Cardias, R; Szilva, A; Di Marco, I; Katsnelson, M I; Lichtenstein, A I; Nordström, L; Klautau, A B; Eriksson, O
2016-05-27
By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions. PMID:27284671
Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe
NASA Astrophysics Data System (ADS)
Kvashnin, Y. O.; Cardias, R.; Szilva, A.; Di Marco, I.; Katsnelson, M. I.; Lichtenstein, A. I.; Nordström, L.; Klautau, A. B.; Eriksson, O.
2016-05-01
By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3 d orbitals of Eg and T2 g symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T2 g orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the Eg states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among Eg states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.
Proportionality of the interfacial Dzyaloshinskii-Moriya interaction and the Heisenberg exchange
NASA Astrophysics Data System (ADS)
Nembach, Hans; Shaw, Justin; Weiler, Mathias; Jué, Emilie; Silva, Tom
The Dzyaloshinkii-Moriya interaction (DMI) gives rise to chiral magnetic ordering and a shift of spin-wave frequencies, depending on their propagation direction. We employed Brillouin-Light-Scattering spectroscopy to measure this nonreciprocal frequency shift, which allowed us to directly determine the magnitude of the DMI in a series of Ni80Fe20(t)/Pt thin film bilayers where the thickness t ranged from 1 to 13 nm. It has also been predicted by theory that the DMI is proportional to the Heisenberg exchange for bulk magnetic oxides and metallic spin-glasses. We tested this prediction for our metallic system by independently determining the Heisenberg exchange via fitting the Bloch T3/2-law to the temperature dependence of the magnetization obtained from SQUID magnetometry. We find that the Ni80Fe20 thickness dependence of the DMI and the Heisenberg exchange are identical, which is consistent with the notion that both effects share the same underlying physics. This result will lead us to a deeper understanding of the DMI and related spin-orbitronic effects.-/
Ordering of the Heisenberg spin glass in two dimensions
NASA Astrophysics Data System (ADS)
Kawamura, Hikaru; Yonehara, Hitoshi
2003-10-01
The spin and the chirality orderings of the Heisenberg spin glass in two dimensions with the nearest-neighbour Gaussian coupling are investigated by equilibrium Monte Carlo simulations. Particular attention is paid to the behaviour of the spin and the chirality correlation lengths. In order to observe the true asymptotic behaviour, a fairly large system size L gap 20 (L the linear dimension of the system) appears to be necessary. It is found that both the spin and the chirality order only at zero temperature. At high temperatures, the chiral correlation length stays shorter than the spin correlation length, whereas at lower temperatures below the crossover temperature T×, the chiral correlation length exceeds the spin correlation length. The spin and the chirality correlation-length exponents are estimated above T× to be ngrSG = 0.9 ± 0.2 and ngrCG = 2.1 ± 0.3, respectively. These values are close to the previous estimates on the basis of the domain-wall-energy calculation. Discussion is given about the asymptotic critical behaviour realized below T×.
NMR spin relaxation rates in the Heisenberg bilayer
NASA Astrophysics Data System (ADS)
Mendes, Tiago; Curro, Nicholas; Scalettar, Richard; Paiva, Thereza; Dos Santos, Raimundo R.
One of the striking features of heavy fermions is the fact that in the vicinity of a quantum phase transition these systems exhibit the breakdown of Fermi-liquid behavior and superconductivity. Nuclear magnetic resonance (NMR) expirements play an important role in the study of these phenomena. Measurements of NMR spin relaxation rates and Knight shift, for instance, can be used to probe the electronic spin susceptibility of these systems. Here we studied the NMR response of the Heisenberg bilayer model. In this model, it is well known that the increase of the interplane coupling between the planes, Jperp, supresses the antiferromagnetic order at a quantum critical point (QCP). We use stochastic series expansion (SSE) and the maximum-entropy analytic continuation method to calculate the NMR spin lattice relaxation rate 1 /T1 and the spin echo decay 1 /T2 G as function of Jperp. The spin echo decay, T2 G increases for small Jperp, due to the increase of the order parameter, and then vanishes abruptly in the QCP. The effects of Jperp dilution disorder in the QCP and the relaxation rates are also discussed. This research was supported by the NNSA Grant Number DE-NA 0002908, and Ciência sem fronteiras program/CNPQ.
Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
NASA Astrophysics Data System (ADS)
Schwandt, David; Alet, Fabien; Oshikawa, Masaki
2014-03-01
Every singlet state of a quantum spin-1/2 system can be decomposed into a linear combination of valence bond basis states. The range of valence bonds within this linear combination as well as the correlations between them can reveal the nature of the singlet state and are key ingredients in variational calculations. In this work, we study the bipartite valence bond distributions and their correlations within the ground state of the Heisenberg antiferromagnet on bipartite lattices. In terms of field theory, this problem can be mapped to correlation functions near a boundary. In dimension d ≥2, a nonlinear σ model analysis reveals that at long distances the probability distribution P (r) of valence bond lengths decays as |r|-d-1 and that valence bonds are uncorrelated. By a bosonization analysis, we also obtain P(r )∝|r|-d-1 in d =1 despite the different mechanism. On the other hand, we find that correlations between valence bonds are important even at large distances in d =1, in stark contrast to d ≥2. The analytical results are confirmed by high-precision quantum Monte Carlo simulations in d =1, 2, and 3. We develop a single-projection loop variant of the valence bond projection algorithm, which is well designed to compute valence bond probabilities and for which we provide algorithmic details.
Field dependent spin transport of anisotropic Heisenberg chain
NASA Astrophysics Data System (ADS)
Rezania, H.
2016-04-01
We have addressed the static spin conductivity and spin Drude weight of one-dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg chain in the finite magnetic field. We have investigated the behavior of transport properties by means of excitation spectrum in terms of a hard core bosonic representation. The effect of in-plane anisotropy on the spin transport properties has also been studied via the bosonic model by Green's function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the spin conductivity and spin Drude weight in the gapped field induced spin-polarized phase for various magnetic field and anisotropy parameters. Furthermore we have studied the magnetic field dependence of static spin conductivity and Drude weight for various anisotropy parameters. Our results show the regular part of spin conductivity vanishes in isotropic case however Drude weight has a finite non-zero value and the system exhibits ballistic transport properties. We also find the peak in the static spin conductivity factor moves to higher temperature upon increasing the magnetic field at fixed anisotropy. The static spin conductivity is found to be monotonically decreasing with magnetic field due to increase of energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of spin Drude weight for different magnetic field and various anisotropy parameters.
Approaching the Heisenberg Limit Without Single-Particle Detection
NASA Astrophysics Data System (ADS)
Bentsen, Gregory; Davis, Emily; Schleier-Smith, Monika
2016-05-01
Achieving Heisenberg-limited measurements with ensembles of more than a few particles remains a major outstanding challenge. The problem is two-fold: one must not only prepare a sufficiently sensitive state, but also be able to detect it. While it is commonly assumed that Heisenberg-limited measurement demands single-particle-resolved detection, we propose an alternative approach that bypasses this requirement. We show that the ``one-axis twisting'' interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Even in the presence of dissipation, the protocol significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit, and achieves near-Heisenberg-limited precision in a √{ N}-times shorter evolution than is required to reach the GHZ state. AFOSR, NSF.
Lipschitz control of geodesics in the Heisenberg group.
Berry, Robert Dan
2010-12-01
Monge first posed his (L{sup 1}) optimal mass transfer problem: to find a mapping of one distribution into another, minimizing total distance of transporting mass, in 1781. It remained unsolved in R{sup n} until the late 1990's. This result has since been extended to Riemannian manifolds. In both cases, optimal mass transfer relies upon a key lemma providing a Lipschitz control on the directions of geodesics. We will discuss the Lipschitz control of geodesics in the (subRiemannian) Heisenberg group. This provides an important step towards a potential theoretic proof of Monge's problem in the Heisenberg group.
Gapless chiral spin liquid in a kagome Heisenberg model
NASA Astrophysics Data System (ADS)
Bieri, Samuel; Messio, Laura; Bernu, Bernard; Lhuillier, Claire
2015-08-01
Motivated by recent experiments on the Heisenberg S =1 /2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled antiferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.
The topological basis expression of Heisenberg spin chain
NASA Astrophysics Data System (ADS)
Hu, Taotao; Ren, Hang; Xue, Kang
2013-11-01
In this paper, it is shown that the Heisenberg XY, XXZ, XXX, and Ising model all can be constructed from the Braid group algebra generator and the Temperley-Lieb algebra generator. And a new set of topological basis expression is presented. Through acting on the different subspaces, we get the new nontrivial six-dimensional and four-dimensional Braid group matrix representations and Temperley-Lieb matrix representations. The eigenstates of Heisenberg model can be described by the combination of the set of topological bases. It is worth mentioning that the ground state is closely related to parameter q which is the meaningful topological parameter.
Heisenberg-scaled magnetometer with dipolar spin-1 condensates
NASA Astrophysics Data System (ADS)
Xing, Haijun; Wang, Anbang; Tan, Qing-Shou; Zhang, Wenxian; Yi, Su
2016-04-01
We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of N atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.
Spectrum, symmetries, and dynamics of Heisenberg spin-1/2 chains
NASA Astrophysics Data System (ADS)
Joel, Kira; Kollmar, Davida; Santos, Lea
2013-03-01
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. Here we provide an introduction to the subject by focusing on the time evolution of Heisenberg spin-1/2 chains with couplings between nearest-neighbor sites only. We study how the anisotropy parameter and the symmetries of the model affect its time evolution. Our predictions are based on the analysis of the eigenvalues and eigenstates of the system and then confirmed with actual numerical results.
Systoles on Heisenberg groups with Carnot-Caratheodory metrics
Dontsov, V V
2001-04-30
The systolic properties of the nilmanifolds N{sup 2n+1} associated with the higher Heisenberg groups H{sub 2n+1} are studied. Effective estimates of the systolic constants {sigma}(N{sup 2n+1}) in the Carnot-Caratheodory geometry, as functions of the parameters defining a uniform lattice on H{sub 2n+1}, are obtained.
Thermodynamics of the Heisenberg ferromagnet in an applied magnetic field.
NASA Technical Reports Server (NTRS)
Flax, L.
1972-01-01
The anisotropic-Heisenberg-ferromagnet formalism developed previously is examined to include an applied magnetic field for the isotropic case in the random-phase approximation. Thermodynamic quantities such as magnetization, susceptibility, and the derivative of magnetization with respect to temperature are studied near the Curie point.
NASA Astrophysics Data System (ADS)
Lulek, Barbara; Jakubczyk, Dorota
2003-03-01
A finite Heisenberg magnetic ring with an arbitrary single-node spin and two spin deviations from the ferromagnetic saturation is considered as the system of two Bethe pseudoparticles. The set of all relevant magnetic configurations spans a surface which can be recognised as a Mőbius strip. The dynamics of the system imposes the double twist of all regular orbits of the translation symmetry group.
Study on isotropic Heisenberg interaction for the realization of SWAP {sup ±α} gates
Muthuganesan, R.; Sankaranarayanan, R.; Balakrishnan, S.
2015-06-24
It is known that nonlocal two-qubit gates are geometrically represented by tetrahedron called as Weyl chamber. Two edges of the Weyl chamber are formed by SWAP{sup ±α} family gates with 0 ≤ α ≤ 1. In this work SWAP{sup ±α} are being realized as two spin system with isotropic Heisenberg exchange interaction. The real parameter α is shown to be the function of duration and strength of interaction. Entanglement of the states generated by these two families of gates is studied with concurrence. Significance of time scale in realizing CNOT using SWAP{sup ±1/2} is highlighted.
Simple pulses for universal quantum computation with a Heisenberg ABAB chain
NASA Astrophysics Data System (ADS)
Benjamin, Simon C.
2001-11-01
Recently, Levy has shown that quantum computation may be performed using an ABAB... chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational ``gates'' may be achieved purely by manipulating the spin-spin interaction: he proposes using ``spin-resonance'' techniques involving modulating the interaction strength at high frequency. Here, we establish an alternative: it is possible to perform the elementary gates via simple, nonoscillatory switching of the interaction strength. This approach removes a time ``bottle neck'' in Levy's scheme, so that all elementary operations may now be performed within a time scale of order ħ/(EA-EB).
NASA Astrophysics Data System (ADS)
Sliwa, Katrina
The quantum back-action of the measurement apparatus arising from the Heisenberg uncertainty principle is both a fascinating phenomenon and a powerful way to apply operations on quantum systems. Unfortunately, there are other effects which may overwhelm the Heisenberg back-action. This thesis focuses on two effects arising in the dispersive measurement of superconducting qubits made with two ultra-low-noise parametric amplifiers, the Josephson bifurcation amplifier (JBA) and the Josephson parametric converter (JPC). The first effect is qubit dephasing due to excess photons in the cavity coming from rogue radiation emitted by the first amplifier stage toward the system under study. This problem arises primarily in measurements made with the JBA, where a strong resonant pump tone is traditionally used to provide the energy for amplification. Replacing the single strong pump tone with two detuned pump tones minimized this dephasing to the point where the Heisenberg back-action of measurements made with the JBA could be observed. The second effect is reduced measurement efficiency arising from losses between the qubit and the parametric amplifier. Most commonly used parametric amplifiers operate in reflection, requiring additional lossy, magnetic elements known as circulators both to separate input from output, and to protect the qubits from dephasing due to the amplified reflected signal. This work presents two alternative directional elements, the Josephson circulator, which is both theoretically loss-less and does not rely upon the strong magnetic fields needed for traditional circulators, and the Josephson directional amplifier which does not send any amplified signal back toward the qubit. Both of these elements achieve directionality by interfering multiple parametric processes inside a single JPC, allowing for in-situ switching between the two modes of operation. This brings valuable experimental flexibility, and also makes these devices strong candidates for
NASA Astrophysics Data System (ADS)
Scherer, Daniel D.; Scherer, Michael M.; Khaliullin, Giniyat; Honerkamp, Carsten; Rosenow, Bernd
2014-07-01
We study the quantum many-body instabilities of the t-JK-JH Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-1/2 model is believed to describe the magnetic properties of the layered transition-metal oxide Na2IrO3. We determine the ground state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow equations adapted to the lack of full spin-rotational invariance in the fermionic interactions, here represented by the highly frustrated and anisotropic Kitaev exchange term. Additionally employing a set of the Ward identities for the Kitaev-Heisenberg model, the numerical solution of the flow equations suggests a rich phase diagram emerging upon doping charge carriers into the ground-state manifold (Z2 quantum spin liquids and magnetically ordered phases). We corroborate superconducting triplet p-wave instabilities driven by ferromagnetic exchange and various singlet pairing phases. For filling δ >1/4, the p-wave pairing gives rise to a topological state with protected Majorana edge modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg exchanges, we obtain bond-order instabilities at van Hove filling supported by nesting and density-of-states enhancement, yielding dimerization patterns of the electronic degrees of freedom on the honeycomb lattice. Further, our flow equations are applicable to a wider class of model Hamiltonians.
Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction
NASA Astrophysics Data System (ADS)
Surungan, Tasrief; Bansawang B., J.; Tahir, Dahlang
2016-03-01
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect, and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.
Approaching the Heisenberg Limit without Single-Particle Detection.
Davis, Emily; Bentsen, Gregory; Schleier-Smith, Monika
2016-02-01
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit. PMID:26894711
Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.
Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R
2016-05-13
The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations. PMID:27232041
q-graded Heisenberg algebras and deformed supersymmetries
Ben Geloun, Joseph; Hounkonnou, Mahouton Norbert
2010-02-15
The notion of q-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for q complex number in the unit disk. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary Z{sub 2} grading or Grassmann parity for associative superalgebra and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit q{yields}-1 for which the Arik and Coon deformation [J. Math. Phys. 17, 524 (1976)] of the Heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.
Spin dynamics simulations for a nanoscale Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Hou, Zhuofei; Landau, D. P.; Brown, G.; Stocks, G. M.
2010-03-01
Thermoinduced magnetization(TiM) is a novel response which was predicted to occur in nanoscale antiferromagnetic materials. Extensive Monte Carlo simulations footnotetextG. Brown, A. Janotti, M. Eisenbach, and G. M. Stocks, Phys.Rev.B 72, 140405(2005) have shown that TiM is an intrinsic property of the antiferromagnetic classical Heisenberg model below the Neel temperature. To obtain a fundamental understanding of TiM, spin dynamics(SD) simulations are performed to study the spin wave behavior, which seems to be the cause of TiM. A classical Heisenberg model with an antiferromagnetic nearest-neighbor exchange interaction and uniaxial single-site anisotropy is studied. Simple-cubic lattices with free boundary conditions are used. We employed the fast spin dynamics algorithms with fourth-order Suzuki-Trotter decompositions of the exponential operator. Additional small excitation peaks due to surface effects are found in transverse S(q,w).
Heisenberg-limited sensitivity with decoherence-enhanced measurements.
Braun, Daniel; Martin, John
2011-01-01
Quantum-enhanced measurements use quantum mechanical effects to enhance the sensitivity of the measurement of classical quantities, such as the length of an optical cavity. The major goal is to beat the standard quantum limit (SQL), that is, an uncertainty of order , where N is the number of quantum resources (for example, the number of photons or atoms used), and to achieve a scaling 1/N, known as the Heisenberg limit. So far very few experiments have demonstrated an improvement over the SQL. The required quantum states are generally highly entangled, difficult to produce, and very prone to decoherence. Here, we show that Heisenberg-limited measurements can be achieved without the use of entangled states by coupling the quantum resources to a common environment that can be measured at least in part. The method is robust under decoherence, and in fact the parameter dependence of collective decoherence itself can be used to reach a 1/N scaling.
Spatially frustrated S = 1 Heisenberg antiferromagnet with single ion anisotropy
NASA Astrophysics Data System (ADS)
Pires, A. S. T.
2016-10-01
Using the SU(3) Schwinger boson formalism, I study the S = 1 square lattice Heisenberg antiferromagnet, at zero temperature, with spatially anisotropic nearest-neighbor couplings frustrated by a next-nearest neighbor interaction and single ion anisotropy. The phase diagram at zero temperature is presented. My calculations show two magnetically ordered phases separated by a quantum-disordered region for all values of the anisotropy.
Type-I integrable quantum impurities in the Heisenberg model
NASA Astrophysics Data System (ADS)
Doikou, Anastasia
2013-12-01
Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.
NASA Astrophysics Data System (ADS)
Nataf, Pierre; Mila, Frédéric
2016-04-01
Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg SU (N ) Hamiltonian with several particles per site living in a fully symmetric or antisymmetric representation of SU (N ) . The method, based on the use of standard Young tableaux, takes advantage of the full SU (N ) symmetry, allowing one to work directly in each irreducible representation of the global SU (N ) group. Since the SU (N ) singlet sector is often much smaller than the full Hilbert space, this enables one to reach much larger system sizes than with conventional exact diagonalizations. The method is applied to the study of Heisenberg chains in the symmetric representation with two and three particles per site up to N =10 and up to 20 sites. For the length scales accessible to this approach, all systems except the Haldane chain [SU (2 ) with two particles per site] appear to be gapless, and the central charge and scaling dimensions extracted from the results are consistent with a critical behavior in the SU (N ) level k Wess-Zumino-Witten universality class, where k is the number of particles per site. These results point to the existence of a crossover between this universality class and the asymptotic low-energy behavior with a gapped spectrum or a critical behavior in the SU (N ) level 1 WZW universality class.
Chern-Simons theory for Heisenberg spins on the Kagome Lattice
NASA Astrophysics Data System (ADS)
Kumar, Krishna; Sun, Kai; Fradkin, Eduardo
2015-03-01
We study the problem of Heisenberg spins on the frustrated Kagome lattice using a 2D Jordan-Wigner transformation that maps the spins (hard-core bosons) onto a system of (interacting) fermions coupled to a Chern-Simons gauge field. This mapping requires us to define a discretized version of the Chern-Simons term on the lattice. Using a recently developed result on how to define Chern-Simons theories on a class of planar lattices, we can consistently study spin models beyond the mean-field level and include the effects of fluctuations, which are generally strong in frustrated systems. Here, we apply these results to study magnetization plateau type states on the Kagome lattice in the regime of XY anisotropy. We find that the 1/3 and 2/3 magnetization plateaus are chiral spin liquid states equivalent to a primary Laughlin fractional quantum Hall state of bosons with (spin) Hall conductivity 1/2 1/4 π and semionic excitations. The 5/9 plateau is a chiral spin liquid equivalent to the first Jain descendant. We also consider the spin-1/2 Heisenberg model on the Kagome lattice with a chirality-breaking term on the triangular plaquettes. This situation also leads to a primary Laughlin bosonic fractional quantum Hall type state with filling fraction 1 / 2 .
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.
2014-01-01
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids. PMID:25204626
Modified Heisenberg model for the zig-zag structure in multiferroic RMn2O5
NASA Astrophysics Data System (ADS)
Bahoosh, Safa Golrokh; Wesselinowa, Julia M.; Trimper, Steffen
2015-08-01
The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.
NASA Astrophysics Data System (ADS)
Enjalran, Matthew; Del Maestro, Adrian; Gingras, Michel J. P.
2008-03-01
The rare-earth pyrochlore gadolinium titanate, Gd2Ti2O7, represents an excellent experimental realization of a Heisenberg antiferromagnet (AFM) in a frustrated geometry with weak long-range dipole-dipole interactions (approximately 20% of nearest neighbor AFM exchange). Experiments on Gd2Ti2O7 in a magnetic field reveal a complex phase diagram associated with the breaking of spatial symmetries of the pyrochlore lattice as the field is applied along select symmetry directions. We study a model of classical Heisenberg spins (O(3) symmetry) on a pyrochlore lattice with exchange and dipolar interactions within mean-field theory. Using parameters relevant to the material system, we develop phase diagrams in finite magnetic fields. Our results our compared to experiments on Gd2Ti2O7 (and Gd2Sn2O7).
Global phase diagram of a doped Kitaev-Heisenberg model
Okamoto, Satoshi
2013-01-01
The global phase diagram of a doped Kitaev-Heisenberg model is studied using an $SU(2)$ slave-boson mean-field method. Near the Kitaev limit, $p$-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You {\\it et al.} [Phys. Rev. B {\\bf 86}, 085145 (2012)] irrespective of the sign of the Kitaev interaction. By further doping, a $d$-wave superconducting state appears when the Kitaev interaction is antiferromagnetic, while another $p$-wave superconducting state appears when the Kitaev interaction is ferromagnetic. This $p$-wave superconducting state does not break the time-reversal symmetry as reported by Hyart {\\it et al.} [Phys. Rev. B {\\bf 85}, 140510 (2012)], and such a superconducting state also appears when the antiferromagnetic Kitaev interaction and the ferromagnetic Heisenberg interaction compete. This work, thus, demonstrates the clear difference between the antiferromagnetic Kitaev model and the ferromagnetic Kitaev model when carriers are doped while these models are equivalent in the undoped limit, and how novel superconducting states emerge when the Kitaev interaction and the Heisenberg interaction compete.
Dissipative phases in the one-dimensional Kondo-Heisenberg model
NASA Astrophysics Data System (ADS)
Lobos, Alejandro; Cazalilla, Miguel A.; Chudzinski, Piotr
2012-02-01
Atomic-sized magnetic structures built on clean metallic surfaces are currently under intense investigation [1]. Besides their potential uses in quantum information storage and processing, these systems allow to ask fundamental questions in condensed matter physics. In particular, the interplay between the Kondo effect (i.e., the screening of the atomic magnetic moment by conduction electrons) and Heisenberg exchange interactions between magnetic impurities has been recently investigated with scanning tunneling microscopy (STM) [2]. Inspired by the above developments, we study an one-dimensional chain of S=1/2 Kondo impurities coupled by anisotropic Heisenberg-Ising exchange and embedded in a two-dimensional metallic substrate. Remarkably, in the case of easy-plane exchange, we find a novel quantum phase exhibiting long-range order at zero temperature. We discuss implications of the existence of this phase for possible experiments. References: [1] R. Wiesendanger, RMP 81, 1495 (2009). [2] P. Wahl et al, PRL 98, 056601 (2007) and references therein.
Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet
Fu, Mingxuan; Imai, Takahashi; Han, Tian -Heng; Lee, Young S.
2015-11-06
Here, the kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu_{3}(OH)_{6}Cl_{2}], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χkagome, deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with the magnetic field dependence of χ_{kagome} that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.
The Design of Control Pulses for Heisenberg Always-On Qubit Models
NASA Astrophysics Data System (ADS)
Magyar, Rudolph
2015-03-01
One model for a universal quantum computer is a spin array with constant nearest neighbor interactions and a controlled unidirectional site-specific magnetic field to generate unitary transformations. This system can be described by a Heisenberg spin Hamiltonian and can be simulated for on the order of 50 spins. It has recently been shown that time-dependent density functional inspired methods may be used to relate various spin models of qubits to ones that may be easier to compute numerically allowing potentially the efficient simulation of greater numbers of spins. One of the challenges of such an agenda is the identification of control pulses that produce desired gate operations (CNOT and single qubit phase gates). We apply control theory to design a universal set of pulses for a Heisenberg always-on model Hamiltonian for a few qubits and compare to known pulses when available. We suggest how this approach may be useful to design control pulses in other realistic designs. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94AL85000.
Thermal entanglement of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain.
Ananikian, N S; Ananikyan, L N; Chakhmakhchyan, L A; Rojas, Onofre
2012-06-27
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
NASA Astrophysics Data System (ADS)
Mishra, Utkarsh; Rakshit, Debraj; Prabhu, R.; Sen(De, Aditi; Sen, Ujjwal
2016-08-01
Disordered systems form one of the centrestages of research in many body sciences and lead to a plethora of interesting phenomena and applications. A paradigmatic disordered system consists of a one-dimensional array of quantum spin-1/2 particles, governed by the Heisenberg spin glass Hamiltonian with natural or engineered quenched disordered couplings in an external magnetic field. These systems allow disorder-induced enhancement for bipartite and multipartite observables. Here we show that simultaneous application of independent quenched disorders results in disorder-induced enhancement, while the same is absent with individual application of the same disorders. We term the phenomenon as constructive interference and the corresponding parameter stretches as the Venus regions. Interestingly, it has only been observed for multiparty entanglement and is absent for the single- and two-party physical quantities.
Time-local Heisenberg-Langevin equations and the driven qubit
NASA Astrophysics Data System (ADS)
Whalen, S. J.; Carmichael, H. J.
2016-06-01
The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg-Langevin equation. Extension to the driven qubit fails—except for weak excitation—due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.
Q-operators for the open Heisenberg spin chain
NASA Astrophysics Data System (ADS)
Frassek, Rouven; Szécsényi, István M.
2015-12-01
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
Spin transport of weakly disordered Heisenberg chain at infinite temperature
NASA Astrophysics Data System (ADS)
Khait, Ilia; Gazit, Snir; Yao, Norman Y.; Auerbach, Assa
2016-06-01
We study the disordered Heisenberg spin chain, which exhibits many-body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as C ˜t-β , whereas the conductivity exhibits a low-frequency power law σ ˜ωα . The exponents depict subdiffusive behavior β <1 /2 ,α >0 at all finite disorders and convergence to the scaling result α +2 β =1 at large disorders.
Spin transport in a one-dimensional anisotropic Heisenberg model.
Znidarič, Marko
2011-06-01
We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Δ is varied spin transport changes from ballistic for Δ<1 to anomalous at the isotropic point Δ=1, to diffusive for finite Δ>1, ending up as a perfect isolator in the Ising limit of infinite Δ. Using perturbation theory for large Δ a quantitative prediction is made for the dependence of diffusion constant on Δ. PMID:21702588
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.
Emergent criticality and Friedan scaling in a two-dimensional frustrated Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Orth, Peter P.; Chandra, Premala; Coleman, Piers; Schmalian, Jörg
2014-03-01
We study a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of triangular and dual honeycomb lattice sites. In the classical ground state, the spins on different sublattices are decoupled, but quantum and thermal fluctuations drive the system into a coplanar state via an "order from disorder" mechanism. We obtain the finite temperature phase diagram using renormalization group approaches. In the coplanar regime, the relative U(1) phase between the spins on the two sublattices decouples from the remaining degrees of freedom, and is described by a six-state clock model with an emergent critical phase. At lower temperatures, the system enters a Z6 broken phase with long-range phase correlations. We derive these results by two distinct renormalization group approaches to two-dimensional magnetism: Wilson-Polyakov scaling and Friedan's geometric approach to nonlinear sigma models where the scaling of the spin stiffnesses is governed by the Ricci flow of a 4D metric tensor.
Strong equivalence principle in polymer quantum mechanics and deformed Heisenberg algebra
NASA Astrophysics Data System (ADS)
Kajuri, Nirmalya
2016-10-01
The strong equivalence principle (SEP) states that the description of a physical system in a gravitational field is indistinguishable from the description of the same system at rest in an accelerating frame. While this statement holds true in both general relativity and ordinary quantum mechanics, one expects it to fail when quantum gravity corrections are taken into account. In this paper we investigate the possible failure of the SEP in two quantum gravity inspired modifications of quantum mechanics—polymer quantum mechanics and deformed Heisenberg algebra. We find that the SEP fails to hold in both these theories. We estimate the deviation from SEP and find in both cases that it is too small to be measured in present day experiments.
Chen Zhixin; Zhou Zhengwei; Zhou Xingxiang; Zhou Xiangga; Guo Guangcan
2010-02-15
We propose a scheme to simulate one-dimensional XXZ-type Heisenberg spin models with competing interactions between nearest neighbors (NNs) and next NNs in photon-coupled microcavities. Our scheme exploits the rich resources and flexible controls available in such a system to realize arbitrarily adjustable ratios between the effective NN and next-NN coupling strengths. Such a powerful capability allows us to simulate frustration phenomena and disorder behaviors in one-dimensional systems arising from next-NN interactions, a large class of problems of great importance in condensed-matter physics. Our scheme is robust due to the lack of atomic excitations, which suppresses spontaneous emission and cavity decay strongly.
Quasiparticle interactions in frustrated Heisenberg chains
NASA Astrophysics Data System (ADS)
Vanderstraeten, Laurens; Haegeman, Jutho; Verstraete, Frank; Poilblanc, Didier
2016-06-01
Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.
Quantum correlations and coherence in spin-1 Heisenberg chains
NASA Astrophysics Data System (ADS)
Malvezzi, A. L.; Karpat, G.; ćakmak, B.; Fanchini, F. F.; Debarba, T.; Vianna, R. O.
2016-05-01
We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.
Fermionology in the Kondo-Heisenberg model: the case of CeCoIn5
NASA Astrophysics Data System (ADS)
Zhong, Yin; Zhang, Lan; Lu, Han-Tao; Luo, Hong-Gang
2015-09-01
The Fermi surface of heavy electron systems plays a fundamental role in understanding their variety of puzzling phenomena, for example, quantum criticality, strange metal behavior, unconventional superconductivity and even enigmatic phases with yet unknown order parameters. The spectroscopy measurement of the typical heavy fermion superconductor CeCoIn5 has demonstrated multi-Fermi surface structure, which has not been studied in detail theoretically in a model system like the Kondo-Heisenberg model. In this work, we take a step toward such a theoretical model by revisiting the Kondo-Heisenberg model. It is found that the usual self-consistent calculation cannot reproduce the fermionology of the experimental observation of the system due to the sign binding between the hopping of the conduction electrons and the mean-field valence-bond order. To overcome such inconsistency, the mean-field valence-bond order is considered as a free/fitting parameter to correlate them with real-life experiments as performed in recent experiments [M.P. Allan, F. Massee, D.K. Morr, J. Van Dyke, A.W. Rost, A.P. Mackenzie, C. Petrovic, J.C. Davis, Nat. Phys. 9, 468 (2013); J. Van Dyke, F. Massee, M.P. Allan, J.C. Davis, C. Petrovic, D.K. Morr, Proc. Natl. Acad. Sci. 111, 11663 (2014)], which also explicitly reflects the intrinsic dispersion of local electrons observed in experimental measurements. Given the fermionology, the calculated effective mass enhancement, entropy, superfluid density and Knight shift are all in qualitative agreement with the experimental results of CeCoIn5, which confirms our assumption. Our result supports a d_{x^2 - y^2 }-wave pairing structure in the heavy fermion material CeCoIn5.
Phase transition of anisotropic frustrated Heisenberg model on the square lattice.
Hu, Ai-Yuan; Wang, Huai-Yu
2016-01-01
We have investigated the J_{1}-J_{2} Heisenberg model with exchange anisotropy on a square lattice and focused on possible AF1-AF2 phase transition below the Néel point and its dependence on the exchange anisotropy, where AF1 and AF2 represent Néel state and collinear state, respectively. We use the double-time Green's-function method and adopt the random-phase approximation. The less the exchange anisotropy, the stronger the quantum fluctuation of the system will be. Both the Néel state and collinear state can exist and have the same Néel temperature for arbitrary anisotropy and spin quantum number S when J_{2}/J_{1}=0.5. Under such parameters, the calculated free energies show that there may occur a first-order phase transition between the Néel state and collinear state for an arbitrary S when anisotropy is not strong. PMID:26871025
Heisenberg spin exchange effects in powder spectra of weakly perturbed triplet states
NASA Astrophysics Data System (ADS)
Chesnut, D. B.; Meinholtz, Dore C.
1985-12-01
Heisenberg spin exchange effects on the powder spectra of weakly perturbed triplet states have been studied by simulation techniques. From very small exchange frequencies on, the derivative powder spectrum is dominated by a sharp, essentially constant width, central line whose amplitude exhibits very close to a square-root dependence on the exchange frequency. The derivative powder edge lines are shown to behave according to the single crystal limiting exchange width equation and it is shown that the frequency dependence of the central dominating line provides yet another measure of exchange parameters in physical systems. Application of these methods to the (φ3AsCH+3) (TCNQ)-2 ion radical salt yields results in good agreement with those obtained by other methods.
Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances.
Ma, Wenchao; Ma, Zhihao; Wang, Hengyan; Chen, Zhihua; Liu, Ying; Kong, Fei; Li, Zhaokai; Peng, Xinhua; Shi, Mingjun; Shi, Fazhan; Fei, Shao-Ming; Du, Jiangfeng
2016-04-22
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.
Magnetic Properties of a Heisenberg Coupled-Trimer Molecular Magnet: General
Haraldsen, Jason T; Barnes, Ted {F E }; Sinclair IV, John W; Thompson, James R; Sacci, Robert L.; Turner, John F. C.
2009-01-01
We report predictions for the energy eigenstates and inelastic neutron scattering excitations of an isotropic Heisenberg hexamer consisting of general spin S and S′ trimers. Specializing to spin-1/2 ions, we give analytic results for the energy excitations, magnetic susceptibility, and inelastic neutron scattering intensities for this hexamer system. To examine this model further, we compare these calculations to the measured magnetic susceptibility of a vanadium material, which is considered to be well defined magnetically as an isolated S = 1/2 V4+ trimer model. Using our model, we determine the amount of inter-trimer coupling that can be accommodated by the measured susceptibility, and predict the inelastic neutron scattering spectrum for comparison with future measurements.
Phase diagram of the classical Heisenberg model in a trimodal random field distribution
NASA Astrophysics Data System (ADS)
Santos-Filho, A.; Albuquerque, D. F. de; Santos-Filho, J. B.; Batista, T. S. Araujo
2016-11-01
The classical spin 1 / 2 Heisenberg model on a simple cubic lattice, with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field, is investigated by effective field theory based on two-spin cluster. The random field is drawn from the asymmetric and anisotropic trimodal probability distribution. The fluctuating bond is extracted from the symmetric and anisotropic bimodal probability. We estimate the transition temperatures, and the phase diagram in the Tc- h, Tc- p and Tc - α planes. We observe that the temperature of the tricritical point decreases with the increase of disorder in exchange interactions until the system ceases to display tricritical behavior. The disorder of the interactions and reentrant phenomena depends on the trimodal distribution of the random field.
NASA Astrophysics Data System (ADS)
Liu, Guang-Hua; Tian, Guang-Shan
2012-08-01
The matrix product state (MPS) is utilized to investigate the ground state properties and quantum phase transitions (QPTs) of the dimerized antiferromagnetic Heisenberg (DAH) model. The ground state MPS wavefunctions determined by the infinite time-evolving block decimation (iTEBD) algorithm are shown to be very efficient descriptions of DAH model. In the thermodynamic limit, the quantum entanglement, the bond energy, and the nearest-neighbor correlations are calculated. It is revealed that the singular behavior of the bipartite entanglement can detect the QPTs directly. The critical point Jc2 = 1.0 is determined evidently, and the quantum phase transition is argued to belong to the second-order category. At the critical point, logarithmic divergent character of the block entanglement is observed, and the system can be described by a free bosonic field theory.
Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances.
Ma, Wenchao; Ma, Zhihao; Wang, Hengyan; Chen, Zhihua; Liu, Ying; Kong, Fei; Li, Zhaokai; Peng, Xinhua; Shi, Mingjun; Shi, Fazhan; Fei, Shao-Ming; Du, Jiangfeng
2016-04-22
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously. PMID:27152779
Order in the Heisenberg pyrochlore: The magnetic structure of Gd2Ti2O7
NASA Astrophysics Data System (ADS)
Champion, J. D. M.; Wills, A. S.; Fennell, T.; Bramwell, S. T.; Gardner, J. S.; Green, M. A.
2001-10-01
The rare-earth pyrochlore material Gd2Ti2O7 is considered to be an ideal model frustrated Heisenberg antiferromagnet with additional dipolar interactions. For this system there are several untested theoretical predictions of the ground state ordering pattern. Here we establish the magnetic structure of isotopically enriched 160Gd2Ti2O7, using powder neutron diffraction at a temperature of 50 mK. The magnetic structure at this temperature is a partially ordered, noncollinear antiferromagnetic structure, with propagation vector k=121212. It can be described as a set of ``q=0'' ordered kagomé planes separated by zero interstitial moments. This magnetic structure agrees with theory only in part, leaving an interesting problem for future research.
Nishimoto, Satoshi; Shibata, Naokazu; Hotta, Chisa
2013-01-01
Quantum spin-1/2 kagome Heisenberg antiferromagnet is the representative frustrated system possibly hosting a spin liquid. Clarifying the nature of this elusive topological phase is a key challenge in condensed matter; however, even identifying it still remains unsettled. Here we apply a magnetic field and discover a series of spin-gapped phases appearing at five different fractions of magnetization by means of a grand canonical density matrix renormalization group, an unbiased state-of-the-art numerical technique. The magnetic field dopes magnons and first gives rise to a possible Z₃ spin liquid plateau at 1/9 magnetization. Higher field induces a self-organized super-lattice unit, a six-membered ring of quantum spins, resembling an atomic orbital structure. Putting magnons into this unit one by one yields three quantum solid plateaus. We thus find that the magnetic field could control the transition between various emergent phases by continuously releasing the frustration.
Nishimoto, Satoshi; Shibata, Naokazu; Hotta, Chisa
2013-01-01
Quantum spin-1/2 kagome Heisenberg antiferromagnet is the representative frustrated system possibly hosting a spin liquid. Clarifying the nature of this elusive topological phase is a key challenge in condensed matter; however, even identifying it still remains unsettled. Here we apply a magnetic field and discover a series of spin-gapped phases appearing at five different fractions of magnetization by means of a grand canonical density matrix renormalization group, an unbiased state-of-the-art numerical technique. The magnetic field dopes magnons and first gives rise to a possible Z₃ spin liquid plateau at 1/9 magnetization. Higher field induces a self-organized super-lattice unit, a six-membered ring of quantum spins, resembling an atomic orbital structure. Putting magnons into this unit one by one yields three quantum solid plateaus. We thus find that the magnetic field could control the transition between various emergent phases by continuously releasing the frustration. PMID:23912842
NASA Astrophysics Data System (ADS)
Yamamoto, Shoji
2000-01-01
In response to recent proton spin-relaxation time measurements on NiCu(pba)(H2O)3.2H2O with pba=1,3-propylenebis(oxamato), which is an excellent one-dimensional ferrimagnetic Heisenberg model system of spin (1,12), we study the Raman relaxation process in spin-(S,s) quantum ferrimagnets on the assumption of predominantly dipolar hyperfine interactions between protons and magnetic ions. The relaxation time T1 is formulated within the spin-wave theory and is estimated as a function of temperature and an applied field H by a quantum Monte Carlo method. The low-temperature behavior of the relaxation rate T-11 qualitatively varies with (S,s), while T-11 is almost proportional to H-1/2 due to the characteristic dispersion relations.
Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances
NASA Astrophysics Data System (ADS)
Ma, Wenchao; Ma, Zhihao; Wang, Hengyan; Chen, Zhihua; Liu, Ying; Kong, Fei; Li, Zhaokai; Peng, Xinhua; Shi, Mingjun; Shi, Fazhan; Fei, Shao-Ming; Du, Jiangfeng
2016-04-01
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.
Magnetic correlations beyond the Heisenberg model in an Fe monolayer on Rh(0 0 1)
NASA Astrophysics Data System (ADS)
Deák, A.; Palotás, K.; Szunyogh, L.; Szabó, I. A.
2015-04-01
Motivated by a recent experimental observation of a complex magnetic structure (Takada et al 2013 J. Magn. Magn. Mater. 329 95) we present a theoretical study of the magnetic structure of an Fe monolayer deposited on Rh(0 0 1). We use a classical spin Hamiltonian with parameters obtained from ab initio calculations and go beyond the usual anisotropic Heisenberg model by including isotropic biquadratic interactions. Zero-temperature Landau-Lifshitz-Gilbert spin dynamics simulations lead to a complex collinear spin configuration that, however, contradicts experimental findings. We thus conclude that higher order multi-spin interactions are likely needed to account for the magnetic ordering of the system.
Cao Min; Zhu Shiqun
2005-03-01
The concurrence of two alternate qubits in a four-qubit Heisenberg XX chain is investigated when a uniform magnetic field B is included. It is found that there is no thermal entanglement between alternate qubits if B is close to zero. A magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic cases. Near zero temperature, the entanglement undergoes two sudden changes with increasing value of the magnetic field B. This is due to the changes in the ground state. This novel property may be used as a quantum entanglement switch. The anisotropy in the system can also induce the entanglement between two alternate qubits.
Existence of Néel Order in the S=1 Bilinear-Biquadratic Heisenberg Model via Random Loops
NASA Astrophysics Data System (ADS)
Lees, Benjamin
2016-10-01
We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relation to quantum spin systems is proved. Using this relation it is shown that for dimensions 3 and above Néel order occurs for a large range of values of the relative strength of the bilinear (- J 1) and biquadratic (- J 2) interaction terms. The proof uses the method of reflection positivity and infrared bounds. Links between spin correlations and loop correlations are proved.
Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G
2009-07-01
We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.
Thermal and magnetic quantum discord in Heisenberg models
Werlang, T.; Rigolin, Gustavo
2010-04-15
We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional XYZ Heisenberg chain in thermal equilibrium depend on the temperature T of the bath and also on an external magnetic field B. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with T when entanglement decreases, cases where QD increases with T even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite T. We also show that by properly tuning B or the interaction between the qubits we get nonzero QD for any T and we present an effect not seen for entanglement, the 'regrowth' of thermal QD.
Local Spin Relaxation within the Random Heisenberg Chain
NASA Astrophysics Data System (ADS)
Herbrych, J.; Kokalj, J.; Prelovšek, P.
2013-10-01
Finite-temperature local dynamical spin correlations Snn(ω) are studied numerically within the random spin-1/2 antiferromagnetic Heisenberg chain. The aim is to explain measured NMR spin-lattice relaxation times in BaCu2(Si0.5Ge0.5)2O7, which is the realization of a random spin chain. In agreement with experiments we find that the distribution of relaxation times within the model shows a very large span similar to the stretched-exponential form. The distribution is strongly reduced with increasing T, but stays finite also in the high-T limit. Anomalous dynamical correlations can be associated with the random singlet concept but not directly with static quantities. Our results also reveal the crucial role of the spin anisotropy (interaction), since the behavior is in contrast with the ones for the XX model, where we do not find any significant T dependence of the distribution.
Fitting magnetic field gradient with Heisenberg-scaling accuracy
Zhang, Yong-Liang; Wang, Huan; Jing, Li; Mu, Liang-Zhu; Fan, Heng
2014-01-01
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements. PMID:25487218
Heisenberg-limited atom clocks based on entangled qubits.
Kessler, E M; Kómár, P; Bishof, M; Jiang, L; Sørensen, A S; Ye, J; Lukin, M D
2014-05-16
We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.
Werner Heisenberg zum 100. Geburtstag: Pionier der Quantenmechanik
NASA Astrophysics Data System (ADS)
Jacobi, Manfred
2001-11-01
Werner Heisenberg war eine der prägendsten Gestalten der Physik des 20. Jahrhunderts. Zu seinen wichtigsten Verdiensten gehören die Grundlegung der Quantenmechanik, die Formulierung der Unschärferelationen sowie die Beteiligung an der Ausarbeitung der Kopenhagener Deutung der Quantenmechanik. Darüber hinaus lieferte er Arbeiten von fundamentalem Charakter zur Theorie des Atomkerns, zur kosmischen Strahlung und zur Quantenfeldtheorie. Während des Krieges war er an den Arbeiten des Uranvereins beteiligt, der die Möglichkeit einer Entwicklung von Kernwaffen untersuchte, jedoch über Vorarbeiten zur Reaktorphysik nicht hinauskam. Wegen dieser Tätigkeit wurde er bei Kriegsende für einige Monate in England interniert. Nach seiner Rückkehr widmete er sich vor allem dem Aufbau der Physik in Deutschland, die während der NS-Zeit nahezu ihrer gesamten Substanz beraubt worden war.
3D Ordering in 2D Quantum Heisenberg Antiferromagnets
NASA Astrophysics Data System (ADS)
Landee, C. P.; Woodward, F. M.; Giantsidis, J.; Turnbull, M. M.
2000-03-01
The family of 2D quantum Heisenberg antiferromagnets (5-ZAP)_2CuX4 consists of CuX_4^2- dianions packed together in magnetically square layers, interacting through X\\cdotsX contacts (X = Cl, Br). The strength of both the intralayer interaction J and interlayer interaction J^' are controlled by the substituent Z in the 5-position of 5-Z, 2-aminopyridine. The 3D critical temperature TN is a function of the J^'/J ratio and consequently is also subject to control by the Z-substituent. Previously we have reported on the compounds with Z = Cl (5-CAP), and Z = methyl (5-MAP). We have now prepared the isomorphous 5-bromo analogue (5-BAP)_2CuX4 and will discuss the T_N/J ratios for all three compounds in terms of the structural parameters.
The elusive Heisenberg limit in quantum-enhanced metrology.
Demkowicz-Dobrzański, Rafał; Kołodyński, Jan; Guţă, Mădălin
2012-01-01
Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. PMID:22990859
Heisenberg-limited atom clocks based on entangled qubits.
Kessler, E M; Kómár, P; Bishof, M; Jiang, L; Sørensen, A S; Ye, J; Lukin, M D
2014-05-16
We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time. PMID:24877919
Energy dynamics in the Heisenberg-Kitaev spin chain
NASA Astrophysics Data System (ADS)
Steinigeweg, Robin; Brenig, Wolfram
2016-06-01
We study the Heisenberg-Kitaev spin chain in order to uncover the interplay between two qualitatively different integrable points in the physics of heat transport in one dimension. Focusing on high temperatures and using analytical as well as numerical approaches within linear response theory, we explore several directions in parameter space including exchange-coupling ratios, anisotropies, and external magnetic fields. We show the emergence of purely ballistic energy transport at all integrable points, manifest in pronounced Drude weights and low-frequency suppression of regular-conductivity contributions. Moreover, off integrability, we find extended quantum chaotic regions with vanishing Drude weights and well-defined dc conductivities. In the vicinity of the Kitaev point, we observe clear signatures of the topological gap in the response function. This gap coexists with a nonzero Drude weight in the Kitaev chain.
NASA Astrophysics Data System (ADS)
Verkholyak, Taras; Strečka, Jozef
2016-10-01
The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaus at zero, one-quarter, and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gapless Luttinger spin-liquid phase. It is evidenced that the approximate results obtained from the strong-coupling approach are in an excellent agreement with the state-of-the-art numerical data obtained for the spin-1/2 Heisenberg orthogonal-dimer chain within the exact diagonalization and density-matrix renormalization group method. The nature of individual quantum ground states is comprehensively studied within the developed perturbation theory.
Heisenberg antiferromagnetic chain with multiple spin 1/2 particles of different flavors per site
NASA Astrophysics Data System (ADS)
Duki, Solomon F.; Yu, Yi-Kuo
Motivated by the discoveries of quasi-1D magnetic systems, we studied a quantum mechanical spin lattice system consisting of a one-dimensional antiferromagnetic Heisenberg chain. In this system we considered M spin 1/2 particles of different flavors per site, and the low-lying states, ground state included, of the Hamiltonian was solved numerically using the exact diagonalization method for finite cluster sizes. We have also obtained the corresponding solutions for systems of the same chain length but with one spin M/2 particle per site. The low energy spectra of both systems are then compared. For M = 2 and M =3, our result shows that the two spin chain systems (one spin M/2 per site vs. M spin 1/2 of different flavors per site) have the same excitation spectra at low energy and the number of overlapped states increases as the size of the cluster increases. The observed overlap also indicates that low energy excitations of the M flavored spin 1/2 chain system selects the high spin states, effectively satisfying the Hund's Rule even though the system does not possess the orbital angular momentum. This work was supported by the Intramural Research Program of the National Library of Medicine at the National Institutes of Health.
NASA Astrophysics Data System (ADS)
Wang, M.; Marshall, R. A.; Edmonds, K. W.; Rushforth, A. W.; Campion, R. P.; Gallagher, B. L.
2016-05-01
We present detailed studies of critical behavior in the strongly site-disordered dilute ferromagnetic semiconductor (Ga,Mn)As. (Ga,Mn)As has a low saturation magnetization and relatively strong magnetocrystalline anisotropy. This combination of properties inhibits domain formation, thus removing a principal experimental difficulty in determining the critical coefficients β and γ . We find that there are still a large number of problems to overcome in terms of measurement procedures and methods of analysis. In particular, the combined effects of disorder and inhomogeneity limit the accessible critical region. However, we find that accurate and reproducible values of the critical exponents β and γ can be obtained from Kouvel-Fisher plots of remanent magnetization and magnetic susceptibility for our (Ga,Mn)As samples. The values of β and γ obtained are consistent with those of the three-dimensional Heisenberg class, despite the very strong disorder present in this system, and they are inconsistent with mean field behavior. Log-log plots of M (H ) data for our samples are consistent with the three-dimensional Heisenberg value of the critical exponent δ , but accurate values of δ could not be obtained for our samples from these plots. We also find that accurate values of the critical exponent α could not be obtained by fitting to the measured temperature derivative of resistivity for our samples. We find that modified Arrott plots and scaling plots are not a practical way to determine the universality class or critical exponents, though they are found to be in better agreement with three-dimensional Heisenberg values than mean field values. Below the critical temperature range, we find that the magnetization shows power-law behavior down to a reduced temperature of t ˜0.5 , with a critical exponent β ˜0.4 , a value appreciably lower than the mean field value of β =0.5 . At lower temperatures, Bloch 3/2 law behavior is observed due to magnons.
Density matrix renormalization group study of triangular Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Sota, Shigetoshi; Sjinjo, Kazuya; Shirakawa, Tomonori; Tohyama, Takami; Yunoki, Seiji
2015-03-01
Topological insulator has been one of the most active subjects in the current condensed matter physics. For most of topological insulators electron correlations are considered to be not essential. However, in the case where electron correlations are strong, novel phases such as a spin liquid phase can emerge in competition with a spin-orbit coupling. Here, using the density matrix renormalization group method, we investigate magnetic phase of a triangular Kitaev-Heisenberg (quantum compass) model that contains a spin-orbital interaction and spin frustration in the antiferromagnetic region. The triangular Kitaev-Heisenberg model is regarded as a dual model of the honeycomb Kitaev-Heisenberg model that is usually employed to discuss A2CuO3 (A=Na, K). Systematically calculating ground state energy, entanglement entropy, entanglement spectrum, and spin-spin correlation functions, we discuss the duality between the triangular and the honeycomb Kitaev-Heisenberg model as well as the ground state magnetic phases.
Employing Taylor and Heisenberg subfilter viscosities to simulate turbulent statistics in LES models
NASA Astrophysics Data System (ADS)
Degrazia, G. A.; Rizza, U.; Puhales, F. S.; Welter, G. S.; Acevedo, O. C.; Maldaner, S.
2012-02-01
A turbulent subfilter viscosity for Large Eddy Simulation (LES) based on the Taylor statistical diffusion theory is proposed. This viscosity is described in terms of a velocity variance and a time scale, both associated to the inertial subrange. This new subfilter viscosity contains a cutoff wavenumber kc, presenting an identical form (differing by a constant) to the Heisenberg subfilter viscosity. Therefore, both subfilter viscosities are described in terms of a sharp division between large and small wavenumbers of a turbulent flow and, henceforth, Taylor and Heisenberg subfilter viscosities are in agreement with the sharp Fourier filtering operation, frequently employed in LES models. Turbulent statistics of different orders, generated from atmospheric boundary layer simulations employing both Taylor and Heisenberg subfilter viscosities have been compared with observations and results provided by other simulations. The comparison shows that the LES model utilizing the approaches of Taylor and Heisenberg reproduces these turbulent statistics correctly in different vertical regions of a planetary convective boundary layer (CBL).
NASA Astrophysics Data System (ADS)
Sadiek, Gehad; Almalki, Samaher
2016-07-01
We consider a finite one-dimensional Heisenberg XYZ spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constraint in presence of an external magnetic field with closed and open boundary conditions. We present an exact numerical solution for the Lindblad master equation of the system in the Liouville space. The dynamics and asymptotic behavior of the nearest-neighbor and beyond-nearest-neighbor pairwise entanglements in the system are investigated under the effect of spatial anisotropy, temperature, system size, and different initial states. The entanglements in the free spin system exhibit nonuniform oscillatory behavior that varies significantly depending on the system size, anisotropy, and initial state. The x y spatial anisotropy dictates the asymptotic behavior of the different entanglements in the system under the influence of the environment regardless of the initial state. Higher anisotropy yields higher steady-state value of the nearest-neighbor entanglement whereas a complete isotropy wipes it out. The longer range entanglements respond differently to the anisotropy variation. The anisotropy in the z direction may enhance the entanglements depending on the interplay with the magnetic field applied in the same direction. As the temperature is raised, the steady state of the short-range entanglements is found to be robust within very small nonzero temperature range that depends critically on the spatial anisotropy. Moreover, the end to end entanglement transfer time and speed through the open boundary chain vary considerably based on the degree of anisotropy and temperature of the environment.
Adiabatic demagnetization of the antiferromagnetic spin-1/2 Heisenberg hexagonal cluster
NASA Astrophysics Data System (ADS)
Deb, Moumita; Ghosh, Asim Kumar
2016-05-01
Exact analytic expressions of eigenvalues of the antiferromagnetic spin-1/2 Heisenberg hexagon in the presence of uniform magnetic field have been obtained. Magnetization process, nature of isentrops and properties of magneto caloric effect in terms of adiabatic demagnetization have been investigated. Theoretical results have been used to study the magneto caloric effect of the spin-1/2 Heisenberg hexagonal compound Cu3WO6.
Werner Heisenberg and Carl Friedrich Freiherr von Weizsäcker: A Fifty-Year Friendship*
NASA Astrophysics Data System (ADS)
Cassidy, David C.
2015-03-01
This paper follows Werner Heisenberg and Carl Friedrich von Weizsäcker during their fifty-year friendship from 1926, when they first met in Copenhagen, to Heisenberg's death in Munich in 1976. The relationship underwent profound changes during that period, as did physics, philosophy, and German society and politics, all of which exerted important influences on their lives, work, and interactions with each other. The nature of these developments and their impact are explored in this paper.
The Heisenberg-Euler Lagrangian as an example of an effective field theory
NASA Astrophysics Data System (ADS)
Dittrich, Walter
2014-10-01
We review the beginning of the effective Lagrangian in QED that was first introduced in the literature by W. Heisenberg and H. Euler in 1936. Deviating from their way of calculating the one-loop effective correction to the classical Maxwell Lagrangian, we use Green's functions and adopt the Fock-Schwinger proper-time method. The important role of the Heisenberg-Euler effective Lagrangian is explicitly demonstrated for low-energy photon-photon processes.
Nakane, Kazuya; Kamijo, Takeshi; Ichinose, Ikuo
2011-02-01
In the present paper, we study a spin-1/2 antiferromagnetic (AF) Heisenberg model on layered anisotropic triangular lattice and obtain its phase structure. We use the Schwinger bosons for representing spin operators and also a coherent-state path integral for calculating physical quantities. Finite-temperature properties of the system are investigated by means of the numerical Monte-Carlo simulations. A detailed phase diagram of the system is obtained by calculating internal energy, specific heat, spin correlation functions, etc. There are AF Neel, paramagnetic, and spiral states. Turning on the plaquette term (i.e., the Maxwell term on a lattice) of an emergent U(1) gauge field that flips a pair of parallel spin-singlet bonds, we found that there appears a phase that is regarded as a deconfined spin-liquid state, though 'transition' to this phase from the paramagnetic phase is not of second order but a crossover. In that phase, the emergent gauge boson is a physical gapless excitation coupled with spinons. These results support our previous study on an AF Heisenberg model on a triangular lattice at vanishing temperature.
Yangian symmetry in molecule {l_brace}V6{r_brace} and four-spin Heisenberg model
Peng Xubiao; Bai Chengming; Ge Molin
2011-02-15
The symmetry operator Q = Y{sup 2} is introduced to re-describe the Heisenberg spin triangles in the {l_brace}V6{r_brace} molecule, where Y stands for the Yangian operator which can be viewed as special form of Dzyaloshinsky-Moriya (DM) interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that is comprised of four 1/2 -spins commutes with Q, which mean that it possesses Yangian symmetry, we show that the ground state of the Hamiltonian H{sub 4} for the model allows to take the total spin S = 1 by choosing some suitable exchange constants in H{sub 4}. In analogy to the molecule {l_brace}V6{r_brace} where the two triangles interact through Yangian operator we then give the magnetization for the theoretical molecule '{l_brace}V8{r_brace}' model which is comprised of two parallelograms. Following the example of molecule {l_brace}V15{r_brace}, we give another theoretical molecule model regarding the four 1/2 -spins system with total spin S = 1 and predict the local moments to be 9/(10) {mu}{sub B},1/(10) {mu}{sub B},1/(10) {mu}{sub B},9/(10) {mu}{sub B}, respectively.
Modified Heisenberg model for the zig-zag structure in multiferroic RMn{sub 2}O{sub 5}
Bahoosh, Safa Golrokh; Wesselinowa, Julia M.; Trimper, Steffen
2015-08-28
The class of RMn{sub 2}O{sub 5} (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn{sup 4+} and Mn{sup 3+} magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.
Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains.
Liu, Wanguo; Shen, Yang; Fang, Guisheng; Jin, Chongjun
2016-05-18
A mechanism for realizing nonreciprocal elementary excitation of spin wave (SW) is proposed. We study a reference model which describes a magnonic crystal (MC) formed by two Heisenberg chains with a lateral displacement (dislocation) and a longitudinal spacer, and derive a criterion to judge whether the elementary excitation spectra are reciprocal in this ferromagnetic lattice. An analytical method based on the spin precession equation is used to solve the elementary excitation spectra. The solution is related to a key factor, the spatio-temporal structure factor [Formula: see text], which can be directly calculated through the structural parameters. When it keeps invariant under the reversions of the external magnetic field [Formula: see text] and the dislocation [Formula: see text], or one of them, the spectra are reciprocal. Otherwise, the SW possesses nonreciprocal spectra with direction-dependent band edges and exhibits a directional magnetoresistance effect. This criterion can be regarded as a necessary and sufficient condition for the (non)reciprocity in the spin lattice. Besides, this novel lattice provides a prototype for spin diodes and spin logic gates. PMID:27092428
Soft Heisenberg hair on black holes in three dimensions
NASA Astrophysics Data System (ADS)
Afshar, Hamid; Detournay, Stephane; Grumiller, Daniel; Merbis, Wout; Perez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-05-01
Three-dimensional Einstein gravity with a negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near-horizon region of these black holes that lead to a surprisingly simple near-horizon symmetry algebra consisting of two affine u ^(1 ) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-Hawking entropy of Bañados-Teitelboim-Zanelli black holes and "black flower" generalizations. From the near-horizon perspective the conformal generators at asymptotic infinity appear as composite operators, which we interpret in the spirit of black hole complementarity. Another remarkable feature of our boundary conditions is that they are singled out by requiring that the whole spectrum is compatible with regularity at the horizon, regardless of the value of the global charges like mass or angular momentum. Finally, we address black hole microstates and generalizations to cosmological horizons.
Variational Monte Carlo investigation of SU (N ) Heisenberg chains
NASA Astrophysics Data System (ADS)
Dufour, Jérôme; Nataf, Pierre; Mila, Frédéric
2015-05-01
Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have investigated the properties of the SU (N) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with m
Stapp's quantum dualism: The James and Heisenberg model of consciousness
NASA Astrophysics Data System (ADS)
Noyes, H. P.
1994-02-01
Henry Stapp attempts to resolve the Cartesian dilemma by introducing what the author would characterize as an ontological dualism between mind and matter. His model for mind comes from William James' description of conscious events and for matter from Werner Heisenberg's ontological model for quantum events (wave function collapse). His demonstration of the isomorphism between the two types of events is successful, but in the author's opinion fails to establish a monistic, scientific theory. The author traces Stapp's failure to his adamant rejection of arbitrariness, or 'randomness.' This makes it impossible for him (or for Bohr and Pauli before him) to understand the power of Darwin's explanation of biology, let alone the triumphs of modern 'neo-Darwinism.' The author notes that the point at issue is a modern version of the unresolved opposition between Leucippus and Democritus on one side and Epicurus on the other. Stapp's views are contrasted with recent discussions of consciousness by two eminent biologists: Crick and Edelman. They locate the problem firmly in the context of natural selection on the surface of the earth. Their approaches provide a sound basis for further scientific work. The author briefly examines the connection between this scientific (rather than ontological) framework and the new fundamental theory based on bit-strings and the combinatorial hierarchy.
Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains
NASA Astrophysics Data System (ADS)
Liu, Wanguo; Shen, Yang; Fang, Guisheng; Jin, Chongjun
2016-05-01
A mechanism for realizing nonreciprocal elementary excitation of spin wave (SW) is proposed. We study a reference model which describes a magnonic crystal (MC) formed by two Heisenberg chains with a lateral displacement (dislocation) and a longitudinal spacer, and derive a criterion to judge whether the elementary excitation spectra are reciprocal in this ferromagnetic lattice. An analytical method based on the spin precession equation is used to solve the elementary excitation spectra. The solution is related to a key factor, the spatio-temporal structure factor {θk}≤ft(Δ x,B\\right) , which can be directly calculated through the structural parameters. When it keeps invariant under the reversions of the external magnetic field B and the dislocation Δ x , or one of them, the spectra are reciprocal. Otherwise, the SW possesses nonreciprocal spectra with direction-dependent band edges and exhibits a directional magnetoresistance effect. This criterion can be regarded as a necessary and sufficient condition for the (non)reciprocity in the spin lattice. Besides, this novel lattice provides a prototype for spin diodes and spin logic gates.
NASA Astrophysics Data System (ADS)
Sewell, Robert; Napolitano, Mario; Behbood, Naeimeh; Colangelo, Giorgio; Martin Ciurana, Ferran; Mitchell, Morgan; Quantum Information With Cold Atoms and Non-Classical Light Team
2013-05-01
We report a nonlinear alignment-to-orientation conversion (AOC) [PRL 85, 2088 (2000)] measurement of atomic spins that simultaneously shows super-Heisenberg scaling and achieves projection-noise limited sensitivity. Using this technique, we have recently demonstrated conditional spin squeezing of the atomic ensemble, and entanglement-enhanced measurement sensitivity useful for optical magnetometry [PRL 109, 253605 (2012)]. In addition, we use a novel technique to explicitly certify that the measurement fulfills all the conditions required for quantum non-demolition measurement [NJP 14, 085021 (2012)], which is non-trivial in large spin (J > 1/2) systems. Lastly, we demonstrate that the measurement shows super-Heisenberg scaling with photon number due to the nonlinearity of the AOC technique. This scaling was recently demonstrated in a proof-of-principle experiment [Nature 471, 486-489 (2011)], however in this experiment the measurement sensitivity was more than an order of magnitude worse than the projection noise limit. Here we achieve a sensitivity (observed read-out noise) of 990 spins, competitive with the best observed sensitivity in an equivalent linear measurement [PRL 104, 093602 (2010)], and 20 dB more sensitive than the previous best nonlinear measurement. ICREA-Institució Catalana de Recerca i Estudis Avançats.
NASA Astrophysics Data System (ADS)
Ivanov, Nedko B.; Ummethum, Jörg; Schnack, Jürgen
2014-10-01
For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S = 1 and σ = 1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.
Emergent Criticality and Ricci Flow in a 2D Frustrated Heisenberg Model
NASA Astrophysics Data System (ADS)
Orth, Peter P.
2014-03-01
In most systems that exhibit order at low temperatures, the order occurs in the elementary degrees of freedom such as spin or charge. Prominent examples are magnetic or superconducting states of matter. In contrast, emergent order describes the phenomenon where composite objects exhibit longer range correlations. Such emergent order has been suspected to occur in a range of correlated materials. One specific example are spin systems with competing interactions, where long-range discrete order in the relative orientation of spins may occur. Interestingly, this order parameter may induce other phase transitions as is the case for the nematic transition in the iron pnictides. In this talk, we introduce and discuss a system with emergent Z6 symmetry, a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of interpenetrating honeycomb and triangular lattices. The multiple spin stiffnesses can be captured in terms of a four-dimensional metric tensor, and the renormalization group flow of the stiffnesses is described by the Ricci flow of the metric tensor. The key result is a decoupling of an emergent collective degree of freedom given by the relative phase of spins on different sublattices. In particular, our results reveal a sequence of two Berezinskii-Kosterlitz-Thouless phase transitions that bracket a critical phase.
Effects of a space modulation on the behavior of a 1D alternating Heisenberg spin-1/2 model.
Mahdavifar, Saeed; Abouie, Jahanfar
2011-06-22
The effects of a magnetic field (h) and a space modulation (δ) on the magnetic properties of a one-dimensional antiferromagnetic-ferromagnetic Heisenberg spin-1/2 model have been studied by means of numerical exact diagonalization of finite size systems, the nonlinear σ model, and a bosonization approach. The space modulation is considered on the antiferromagnetic couplings. At δ = 0, the model is mapped to a gapless Lüttinger liquid phase by increasing the magnetic field. However, the space modulation induces a new gap in the spectrum of the system and the system experiences different quantum phases which are separated by four critical fields. By opening the new gap, a magnetization plateau appears at ½M(sat). The effects of the space modulation are reflected in the emergence of a plateau in other physical functions such as the F-dimer and the bond-dimer order parameters, and the pair-wise entanglement. PMID:21613724
Petersen, Jakob; Pollak, Eli
2015-12-14
One of the challenges facing on-the-fly ab initio semiclassical time evolution is the large expense needed to converge the computation. In this paper, we suggest that a significant saving in computational effort may be achieved by employing a semiclassical initial value representation (SCIVR) of the quantum propagator based on the Heisenberg interaction representation. We formulate and test numerically a modification and simplification of the previous semiclassical interaction representation of Shao and Makri [J. Chem. Phys. 113, 3681 (2000)]. The formulation is based on the wavefunction form of the semiclassical propagation instead of the operator form, and so is simpler and cheaper to implement. The semiclassical interaction representation has the advantage that the phase and prefactor vary relatively slowly as compared to the “standard” SCIVR methods. This improves its convergence properties significantly. Using a one-dimensional model system, the approximation is compared with Herman-Kluk’s frozen Gaussian and Heller’s thawed Gaussian approximations. The convergence properties of the interaction representation approach are shown to be favorable and indicate that the interaction representation is a viable way of incorporating on-the-fly force field information within a semiclassical framework.
Quantum correlation dynamics in a two-qubit Heisenberg XYZ model with decoherence
NASA Astrophysics Data System (ADS)
Yang, Guo-Hui; Zhang, Bing-Bing; Li, Lei
2015-06-01
Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord (QD). Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented: there is an “entanglement intermittently sudden death” phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter Δ. Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and Δ, whereas the parameter b is independent of the steady concurrence and QD. Project supported by the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2012021003-3) and the Special Funds of the National Natural Science Foundation of China (Grant No. 11247247).
Atanasov, Victor; Saxena, Avadh
2011-05-01
Adopting a purely two-dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting the off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and normal to the surface parts, and in the process the embedding of this surface into the three-dimensional world is accounted for. As a result an invariant geometric potential arises in the surface part which scales linearly with the mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or 'straintronics' is clearly an important field of study in graphene. This opens an avenue to producing electronic devices: micro- and nano-electromechanical systems (MEMS and NEMS), where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks in the curved space-time of general relativity. In this context we explore a two-dimensional cross-section of the wormhole geometry, realized with graphene as a solid state thought experiment.
High Field Magnetization Studies of Low Dimensional Heisenberg S = 1/2 Antiferromagnets
NASA Astrophysics Data System (ADS)
Landee, C. P.; Turnbull, M. M.
1998-03-01
The magnetization curves of a number of low dimensional S=1/2 Heisenberg antiferromagnets have been determined in fields up to 30 tesla at low temperatures at the National High Magnetic Fields Laboratory. Materials studied include a family of 1D materials, based upon Cu(pyrazine)(NO_3)_2, 2D magnets consisting of pyrazine-bridged copper layers, and several spin ladders with singlet ground states. All of the magnetization data show upward curvature and are well described by T = 0 calculations based upon finite cluster models(Bonner and Fisher, Phys. Rev. A135, 640 (1964); Yang and Mutter, NANL cond-mat/9610092.). Chemical substitution on the pyrazine rings permits the variation of exchange constants by more than 25 percent for the family of well isolated chains. The spin ladder systems consist of ferromagnetic dimers weakly connected by antiferromagnetic intradimer interactions. Field induced transitions are seen at fields of less than one tesla for each of the three compounds.
Application of state-multipole Heisenberg equations to Raman excitation dynamics
Shore, B.W.; Sacks, R.; Dixit, S.N.
1987-09-10
Description of detailed temporal excitation dyanmics for coherent excitation, such as is produced by idealized laser radiation, contrasts with evaluation of rate coefficients by means of generalized Golden Rule procedures; it requires an appropriate time-dependent Schroedinger equation. When the atom undergoing excitation is also affected by incoherent processes, such as collisions, this equation no longer suffices. The Heisenberg equations, or equivalent density-matrix equations, permit treatment in which coherence and incoherence play comparable roles in the excitation dynamics. Unlike rate equations, such equations must incorporate complexities that originate in the orientation degeneracy expressed by magnetic quantum numbers. In simple cases of coherent excitation, both for single-photon and multiphoton excitation, the sublevels merely require an average of 2J+1 independent Schroedinger equations. Relaxation couples the independent equations. It has been known for some time that appropriate state-multipole operators can simplify the description of many phenomena connected with optical pumping. This memo discusses application of these multipole operators to the description of Raman (or more general multiphoton) coherent excitation. In some simple limiting cases the equations simplify, but in general one has a hierarchy of coupled multipole polarizations and coherences in place of the populations and coherences that occur as variables in nondegenerate systems. 28 refs., 4 figs.
NASA Astrophysics Data System (ADS)
Souletie, Jean; Drillon, Marc; Rabu, Pierre; Pati, Swapan K.
2004-08-01
The phenomenological expression χT/(Ng2μB2/k)=C1nexp(-W1n/T)+C2nexp(-W2n/T) describes very accurately the temperature dependence of the magnetic susceptibility computed for antiferromagnetic rings of Heisenberg spins S=1 , whose size n is even and ranges from 6 to 20. This expression has been obtained through a strategy justified by scaling considerations together with finite size numerical calculations. For n large, the coefficients of the expression converge towards C1=0.125 , W1=0.451J , C2=0.564 , W2=1.793J ( J is the exchange constant), which are appropriate for describing the susceptibility of the spin-1 Haldane chain. The Curie constant, the paramagnetic Curie-Weiss temperature, the correlation length at T=0 and the Haldane gap are found to be closely related to these coefficients. With this expression, a very good description of the magnetic behavior of Y2BaNiO5 and of Ni(C2H8N2)2NO2ClO4 (NENP), the archetype of the Haldane gap systems, is achieved over the whole temperature range.
NASA Astrophysics Data System (ADS)
McLeod, David; McLeod, Roger
2008-04-01
The electron model used in our other joint paper here requires revision of some foundational physics. That electron model followed from comparing the experimentally proved results of human vision models using spatial Fourier transformations, SFTs, of pincushion and Hermann grids. Visual systems detect ``negative'' electric field values for darker so-called ``illusory'' diagonals that are physical consequences of the lens SFT of the Hermann grid, distinguishing this from light ``illusory'' diagonals. This indicates that oppositely directed vectors of the separate illusions are discretely observable, constituting another foundational fault in quantum mechanics, QM. The SFT of human vision is merely the scaled SFT of QM. Reciprocal space results of wavelength and momentum mimic reciprocal relationships between space variable x and spatial frequency variable p, by the experiment mentioned. Nobel laureate physicist von B'ek'esey, physiology of hearing, 1961, performed pressure input Rect x inputs that the brain always reports as truncated Sinc p, showing again that the brain is an adjunct built by sight, preserves sign sense of EMF vectors, and is hard wired as an inverse SFT. These require vindication of Schr"odinger's actual, but incomplete, wave model of the electron as having physical extent over the wave, and question Heisenberg's uncertainty proposal.
Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field.
Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan
2012-06-27
By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.
Mayhall, Nicholas J.; Head-Gordon, Martin
2014-10-07
We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited (and spin-flipped), from the single reference with maximum S{sup ^}{sub z}, M, to the M − 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one β electron is required, together with only one α hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M − 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed.
Mamiya, Hiroaki; Nimori, Shigeki
2012-04-01
Universality of spin configuration restoration is studied in Heisenberg spin glasses: a dilute magnetic semiconductor Cd{sub 55}Mn{sub 45}Te as well as a dilute magnetic alloy Cu{sub 97}Mn{sub 3}. Reversions of the relaxations of magnetization were observed in both systems undergoing positive/negative temperature cycling under a constant magnetic field. Because the magnetization mirrors evolution of the spin configuration, these reversions indicate that the spin configurations are spontaneously restored to the initially stabilized states when the temperature is returned to the original. Whereas such spin restoration does not occur if the spin glasses are simply frozen, it is possible in the alternative ghost domain scenario of the droplet picture. This finding thus provides fresh insight into the nature of glassy systems.
Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice.
Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris
2016-04-29
We study the low-temperature physics of the SU(2)-symmetric spin-1/2 Heisenberg antiferromagnet on a pyrochlore lattice and find "fingerprint" evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature T/J=1/6. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at T/J=1/6. The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points. PMID:27176537
Near-Heisenberg-limited atomic clocks in the presence of decoherence.
Borregaard, J; Sørensen, A S
2013-08-30
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near-Heisenberg-limited stability of atomic clocks using entangled atoms. The protocol may thus realize the full potential of entanglement for quantum metrology despite the detrimental influence of decoherence.
Low-temperature Spin-Ice State of Quantum Heisenberg Magnets on Pyrochlore Lattice
NASA Astrophysics Data System (ADS)
Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris
We establish that the isotropic spin-1/2 Heisenberg antiferromagnet on pyrochlore lattice enters a spin-ice state at low, but finite, temperature. Our conclusions are based on results of the bold diagrammatic Monte Carlo simulations that demonstrate good convergence of the skeleton series down to temperature T = J/6. The ``smoking gun'' identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for static spin-spin correlation function between the quantum Heisenberg and classical Heisenberg/Ising models at all accessible temperatures. In particular, at T/J = 1/6, the momentum dependence shows a characteristic bow-tie pattern with pinch points. By numerical analytical continuation method, we also obtain the dynamic structure factor at real frequencies, showing a diffusive spinon dynamics at pinch points and spin wave continuum along the nodal lines.?
Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
NASA Astrophysics Data System (ADS)
Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris
2016-04-01
We study the low-temperature physics of the SU(2)-symmetric spin-1 /2 Heisenberg antiferromagnet on a pyrochlore lattice and find "fingerprint" evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature T /J =1 /6 . The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at T /J =1 /6 . The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.
Near-Heisenberg-limited atomic clocks in the presence of decoherence.
Borregaard, J; Sørensen, A S
2013-08-30
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near-Heisenberg-limited stability of atomic clocks using entangled atoms. The protocol may thus realize the full potential of entanglement for quantum metrology despite the detrimental influence of decoherence. PMID:24033016
Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation
Baek, So-Young; Kaneda, Fumihiro; Ozawa, Masanao; Edamatsu, Keiichi
2013-01-01
The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation. PMID:23860715
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1976-01-01
Presented is an insight into man's idea about physics and being a physicist in the days when Heisenberg, P. A. M. Dirac, Louis de Broglic and other famous physicists were young men. Heisenberg is compared to Newton, inventing new math as he needed it. Emphasis is placed on the fact that he was not a Nazi sympathizer. (EB)
Heisenberg-limited interferometry with pair coherent states and parity measurements
Gerry, Christopher C.; Mimih, Jihane
2010-07-15
After reviewing parity-measurement-based interferometry with twin Fock states, which allows for supersensitivity (Heisenberg limited) and super-resolution, we consider interferometry with two different superpositions of twin Fock states, namely, two-mode squeezed vacuum states and pair coherent states. This study is motivated by the experimental challenge of producing twin Fock states on opposite sides of a beam splitter. We find that input two-mode squeezed states, while allowing for Heisenberg-limited sensitivity, do not yield super-resolutions, whereas both are possible with input pair coherent states.
Yao, Xiaoyan; Dong, Shuai
2016-01-01
The expanded classical Kitaev-Heisenberg model on a honeycomb lattice is investigated with the next-nearest-neighboring Heisenberg interaction considered. The simulation shows a rich phase diagram with periodic behavior in a wide parameter range. Beside the double 120° ordered phase, an inhomogeneous phase is uncovered to exhibit a topological triple-vortex lattice, corresponding to the hexagonal domain structure of vector chirality, which is stabilized by the mixed frustration of two sources: the geometrical frustration arising from the lattice structure as well as the frustration from the Kitaev couplings. PMID:27229486
Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment
NASA Astrophysics Data System (ADS)
Jeevanesan, Bhilahari; Chandra, Premala; Coleman, Piers; Orth, Peter P.
2015-10-01
In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multispin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type, and at lower temperatures we find long-range Z6 order.
Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment.
Jeevanesan, Bhilahari; Chandra, Premala; Coleman, Piers; Orth, Peter P
2015-10-23
In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multispin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type, and at lower temperatures we find long-range Z(6) order.
Yao, Xiaoyan; Dong, Shuai
2016-01-01
The expanded classical Kitaev-Heisenberg model on a honeycomb lattice is investigated with the next-nearest-neighboring Heisenberg interaction considered. The simulation shows a rich phase diagram with periodic behavior in a wide parameter range. Beside the double 120° ordered phase, an inhomogeneous phase is uncovered to exhibit a topological triple-vortex lattice, corresponding to the hexagonal domain structure of vector chirality, which is stabilized by the mixed frustration of two sources: the geometrical frustration arising from the lattice structure as well as the frustration from the Kitaev couplings. PMID:27229486
Partition functions of classical Heisenberg spin chains with arbitrary and different exchange
NASA Astrophysics Data System (ADS)
Cregg, P. J.; García-Palacios, J. L.; Svedlindh, P.
2008-10-01
The classical Heisenberg model has been effective in modelling exchange interactions in molecular magnets. In this model, the partition function is important as it allows the calculation of the magnetization and susceptibility. For an ensemble of N-spin sites, this typically involves integrals in 2N dimensions. Here, for two-, three- and four-spin nearest neighbour open linear Heisenberg chains these integrals are reduced to sums of known functions, using a result due to Gegenbauer. For the case of the three- and four-spin chains, the sums are equivalent in form to the results of Joyce. The general result for an N-spin chain is also obtained.
Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction
Lees, Benjamin
2014-09-15
We look at the general SU(2) invariant spin-1 Heisenberg model. This family includes the well-known Heisenberg ferromagnet and antiferromagnet as well as the interesting nematic (biquadratic) and the largely mysterious staggered-nematic interaction. Long range order is proved using the method of reflection positivity and infrared bounds on a purely nematic interaction. This is achieved through the use of a type of matrix representation of the interaction making clear several identities that would not otherwise be noticed. Using the reflection positivity of the antiferromagnetic interaction one can then show that the result is maintained if we also include an antiferromagnetic interaction that is sufficiently small.
NASA Astrophysics Data System (ADS)
Vekua, T.; Sun, G.
2016-07-01
Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-1/2 chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators <
Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach
Roos, P. A.; Murphy, S. K.; Meng, L. S.; Carlsten, J. L.; Ralph, T. C.; White, A. G.; Brasseur, J. K.
2003-07-01
We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump {r_reversible} pump, Stokes {r_reversible} signal, and Raman coherence {r_reversible} idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.
The Taylor spectrum and transversality for a Heisenberg algebra of operators
NASA Astrophysics Data System (ADS)
Dosi, Anar A.
2010-05-01
A problem on noncommutative holomorphic functional calculus is considered for a Banach module over a finite-dimensional nilpotent Lie algebra. As the main result, the transversality property of algebras of noncommutative holomorphic functions with respect to the Taylor spectrum is established for a family of bounded linear operators generating a Heisenberg algebra. Bibliography: 25 titles.
The Taylor spectrum and transversality for a Heisenberg algebra of operators
Dosi, Anar A
2010-05-11
A problem on noncommutative holomorphic functional calculus is considered for a Banach module over a finite-dimensional nilpotent Lie algebra. As the main result, the transversality property of algebras of noncommutative holomorphic functions with respect to the Taylor spectrum is established for a family of bounded linear operators generating a Heisenberg algebra. Bibliography: 25 titles.
Numerical calculations for Heisenberg ferromagnet on honeycomb lattice using Oguchi’s method
Mert, Gülistan; Mert, H. Şevki
2015-03-10
Magnetic properties such as the magnetization, internal energy and specific heat for Heisenberg ferromagnet with spin - 1/2 on honeycomb lattice are have been calculated using Oguchi’s method. We have found that the magnetic specific heat exhibits two peaks.
Fick's law, green-kubo formula, and Heisenberg's equation of motion
Lee
2000-09-18
Fick's law is important in transport theory and nonequilibrium statistical mechanics. The Heisenberg equation of motion for density is examined to see how it could be reduced to the diffusion equation, which is exactly equivalent to Fick's law. Conditions that are required have been noted and their implications explored.
The Role of Logic and Mathematics in the Heisenberg Formulation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Venezia, Antonio
2006-06-01
In this paper, by means of a logical and linguistic analysis of Heisenberg's work, the properties of a logical model suitable for quantum mechanics are obtained. This model is an alternative to traditional quantum logic, because it uses an intuitionist negation. It is able to justify the passage from the problem of conjugate variables measurement to the mathematical formalization (commutation rules) of matrix mechanics.
While Heisenberg Is Not Looking: The Strength of "Weak Measurements" in Educational Research
ERIC Educational Resources Information Center
Geelan, David R.
2015-01-01
The concept of "weak measurements" in quantum physics is a way of "cheating" the Uncertainty Principle. Heisenberg stated (and 85 years of experiments have demonstrated) that it is impossible to know both the position and momentum of a particle with arbitrary precision. More precise measurements of one decrease the precision…
Quasilocal Conserved Operators in the Isotropic Heisenberg Spin-1 /2 Chain
NASA Astrophysics Data System (ADS)
Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž
2015-09-01
Composing higher auxiliary-spin transfer matrices and their derivatives, we construct a family of quasilocal conserved operators of isotropic Heisenberg spin-1 /2 chain and rigorously establish their linear independence from the well-known set of local conserved charges.
Studying the thermally entangled state of a three-qubit Heisenberg XX ring via quantum teleportation
Yeo, Ye
2003-08-01
We consider quantum teleportation as a tool to investigate the thermally entangled state of a three-qubit Heisenberg XX ring. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence of the state. In particular, two mixtures of different pairs of W states, which result in the same concurrence, could yield very different average teleportation fidelities.
Friction factor for turbulent flow in rough pipes from Heisenberg's closure hypothesis.
Calzetta, Esteban
2009-05-01
We show that the main results of the analysis of the friction factor for turbulent pipe flow reported by Gioia and Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying the analysis of Gioia and Chakraborty.
Finite-temperature scaling of spin correlations in a partially magnetized Heisenberg S =1/2 chain
NASA Astrophysics Data System (ADS)
Hälg, M.; Hüvonen, D.; Butch, N. P.; Demmel, F.; Zheludev, A.
2015-09-01
Inelastic neutron scattering is employed to study transverse spin correlations of a Heisenberg S =1 /2 chain compound in a magnetic field of 7.5 T. The target compound is the antiferromagnetic Heisenberg S =1 /2 chain material 2(1,4-dioxane).2 (H2O ).CuCl2, or CuDCl for short. The validity and the limitations of the scaling relation for the transverse dynamic structure factor are tested, discussed, and compared to the Tomonaga-Luttinger spin liquid theory and to Bethe-ansatz results for the Heisenberg model.
NASA Astrophysics Data System (ADS)
Lacki, Jan
2003-09-01
Werner Heisenberg was one of the greatest physicists of the 20th century. He participated as a front rank actor in the shaping of a good part of XXth century physics and directly witnessed most of the intellectual struggles which led to what he called “Wandlungen in den Grundlagen der exakten Naturwissenschaft”. This expression is borrowed from one of the many talks and writings he devoted to the analysis of the scientific and philosophical implications of his, and his fellows physicists, findings. Indeed, Heisenberg's scientific activity increasingly reflected his more general intellectual views. This makes him another magnificent representative of a glorious linage going from the remote times of modern science to Einstein, Bohr and the like. This “philosophical” vein started early in his scientific life, and got stronger with time, prompted by the highly demanding scientific, but also social and political context of his mature years.
Exactly solved mixed spin-(1,1/2) Ising-Heisenberg distorted diamond chain
NASA Astrophysics Data System (ADS)
Lisnyi, Bohdan; Strečka, Jozef
2016-11-01
The mixed spin-(1,1/2) Ising-Heisenberg model on a distorted diamond chain with the spin-1 nodal atoms and the spin-1/2 interstitial atoms is exactly solved by the transfer-matrix method. An influence of the geometric spin frustration and the parallelogram distortion on the ground state, magnetization, susceptibility and specific heat of the mixed-spin Ising-Heisenberg distorted diamond chain are investigated in detail. It is demonstrated that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and one-half of the saturation magnetization. The temperature dependence of the specific heat may have up to three distinct peaks at zero magnetic field and up to four distinct peaks at a non-zero magnetic field. The origin of multipeak thermal behavior of the specific heat is comprehensively studied.
Three-qubit thermal entanglement via entanglement swapping on two-qubit Heisenberg XY chains
Kao, Zi Chong; Ng, Jezreel; Yeo, Ye
2005-12-15
In this paper, we consider the generation of a three-qubit Greenberger-Horne-Zeilinger-like thermal state by applying the entanglement swapping scheme of Zukowski et al. [Ann. N. Y. Acad. Sci. 755, 91 (1995)] to three pairs of two-qubit Heisenberg XY chains. The quality of the resulting three-qubit entanglement is studied by analyzing the teleportation fidelity, when it is used as a resource in the teleportation protocol of Karlsson et al. [Phys. Rev. A 58, 4394 (1998)]. We show that even though thermal noise in the original two-qubit states is amplified by the entanglement swapping process, we are still able to achieve nonclassical fidelities for the anisotropic Heisenberg XY chains at finitely higher and higher temperatures by adjusting the strengths of an external magnetic field. This has a positive implication on the solid-state realization of a quantum computer.
Nontrivial ferrimagnetism of the Heisenberg model on the Union Jack strip lattice
NASA Astrophysics Data System (ADS)
Shimokawa, Tokuro; Nakano, Hiroki
2013-08-01
We study the ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on the Union Jack strip lattice by using the exact-diagonalization and density matrix renormalization group methods. We confirm a region of a magnetization state intermediate between the Néel-like spin liquid state and the conventional ferrimagnetic state of a Lieb-Mattis type. In the intermediate state, we find that the spontaneous magnetization changes gradually with respect to the strength of the inner interaction. In addition, the local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the intermediate magnetization state. These characteristic behaviors lead to the conclusion that the intermediate magnetization state is a non-Lieb-Mattis ferrimagnetic one. We also discuss the relationship between the ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on the original Union Jack lattice and those on our strip lattice.
Zigzag order and phase competition in expanded Kitaev-Heisenberg model on honeycomb lattice
NASA Astrophysics Data System (ADS)
Yao, Xiaoyan
2015-07-01
The Kitaev-Heisenberg model on the honeycomb lattice is investigated in two cases: (I) with the Kitaev interaction between the nearest neighbors, and (II) with the Kitaev interaction between the next nearest neighbors. In the full parameter range, the ground states are searched by Monte Carlo simulation and identified by evaluating the correlation functions. The energies of different phases are calculated and compared with the simulated result to show the phase competition. It is observed from both energy calculation and the density of states that the zigzag order shows a symmetric behavior to the stripy phase in the pure Kitaev-Heisenberg model. By considering more interactions in both cases, the energy of zigzag order can be reduced lower than the energies of other states. Thus the zigzag phase may be stabilized in more parameter region and even extended to the whole parameter range.
NASA Astrophysics Data System (ADS)
Zad, Hamid Arian; Movahhedian, Hossein
2016-08-01
Heat capacity of a mixed-three-spin (1/2,1,1/2) antiferromagnetic XXX Heisenberg chain is precisely investigated by use of the partition function of the system for which, spins (1,1/2) have coupling constant J1 and spins (1/2,1/2) have coupling constant J2. We verify tripartite entanglement for the model by means of the convex roof extended negativity (CREN) and concurrence as functions of temperature T, homogeneous magnetic field B and the coupling constants J1 and J2. As shown in our previous work, [H. A. Zad, Chin. Phys. B 25 (2016) 030303.] the temperature, the magnetic field and the coupling constants dependences of the heat capacity for such spin system have different behaviors for the entangled and separable states, hence, we did some useful comparisons between this quantity and negativities of its organized bipartite (sub)systems at entangled and separable states. Here, we compare the heat capacity of the mixed-three-spin (1/2,1,1/2) system with the CREN and the tripartite concurrence (as measures of the tripartite entanglement) at low temperature. Ground state phase transitions, and also, transition from ground state to some excited states are explained in detail for this system at zero temperature. Finally, we investigate the heat capacity behavior around those critical points in which these quantum phase transitions occur.
A Study of Low-Dimensional S=1/2 Quantum Heisenberg Antiferromagnets; Simulation and Experiment
NASA Astrophysics Data System (ADS)
Keith, Brian C.
We have simulated and analyzed the susceptibility of a series of two-dimensional (2D) spin-½ rectangular Heisenberg antiferromagnetic (as well as mixed exchange antiferromagnetic/ferromagnetic) lattices as a function of J,J' and temperature, where J is the dominant magnetic exchange interaction and J', the orthogonal interaction, is related to J by J' = alpha J, where alpha can vary from 0 to 1. Previous studies of the compounds pyrazineformatocopper(II) nitrate [Cu(pz)( HCO2)](NO3), catena-2-aminopyrimidinedichlorocopper(II) [Cu(2 - apm)Cl 2], and catena-pyrazinediazidocopper(II) [Cu( pz)(N3)2] indicated that these systems had 2D magnetic spin-spin interactions. However, there were no 2D models that could capture the behavior of any measurable bulk properties of the compounds. The previous authors fit the susceptibility data of the respective compounds to a 1D antiferromagnetic chain with a mean field correction, or did not fit the data at all. We use the simulations to create this fit function in order to test the 2D model proposed for these spin systems. The quantum phase transitions of a family of spin ladders, corresponding to the closure of the gap and the polarization of all spins, have been explored through high pulsed field magnetization techniques. Modeling the susceptibility data yields values which were used to simulate the high field magnetization data. The simulations confirm the upper and lower critical fields, with minor discrepancies between data and simulation that probably have to do with the peculiar background subtraction. Also, calculations of the critical fields are within 10% of the observed critical fields. Furthermore, randomness was introduced into the family of spin ladders and interesting effects arose from this doping. For Cu( qnx)(Cl1-xBr x)2, the energy gaps were found to vary little with dopant concentration while the paramagnetic susceptibility at low temperature appeared to be suppressed with increased dopant level. Again, for Cd
A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities
NASA Astrophysics Data System (ADS)
Ludvin Felcy, A.; Latha, M. M.; Christal Vasanthi, C.
2016-10-01
We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.
String limit of the isotropic Heisenberg chain in the four-particle sector
Antipov, A. G. Komarov, I. V.
2008-05-15
The quantum method of variable separation is applied to the spectral problem of the isotropic Heisenberg model. The Baxter difference equation is resolved by means of a special quasiclassical asymptotic expansion. States are identified by multiplicities of limiting values of the Bethe parameters. The string limit of the four-particle sector is investigated. String solutions are singled out and classified. It is shown that only a minor fraction of solutions demonstrate string behavior.
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
NASA Astrophysics Data System (ADS)
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
Correlation functions of the antiferromagnetic Heisenberg model using a modified Lanczos method
NASA Astrophysics Data System (ADS)
Gagliano, Eduardo R.; Dagotto, Elbio; Moreo, Adriana; Alcaraz, Francisco C.
1986-08-01
Using a modified Lanczos algorithm, we study the correlation functions in the ground state of the one-dimensional antiferromagnetic Heisenberg model. We obtain numerical results for rings up to 24 sites. There are no indications of the anomalous behavior of these correlation functions recently observed in chains with 16 sites. We also present a pedagogical description of the hashing technique which is an efficient algorithm for searching and storage purposes.
Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator
Chang, Der-Chen; Li, Yutian
2015-01-01
The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries. PMID:25792966
Teleportation via thermally entangled states of a two-qubit Heisenberg XX chain
Yeo Ye
2002-12-01
Recently, entanglement teleportation has been investigated by Lee and Kim [Phys. Rev. Lett. 84, 4236 (2000)]. In this paper we study entanglement teleportation via two separate thermally entangled states of a two-qubit Heisenberg XX chain. We established the condition under which the parameters of the model have to satisfy in order to teleport entanglement. The necessary minimum amount of thermal entanglement for some fixed strength of exchange coupling is a function of the magnetic field and the temperature.
Heisenberg Uncertainty and the Allowable Masses of the Up Quark and Down Quark
NASA Astrophysics Data System (ADS)
Orr, Brian
2004-05-01
A possible explanation for the inability to attain deterministic measurements of an elementary particle's energy, as given by the Heisenberg Uncertainty Principle, manifests itself in an interesting anthropic consequent of Andrei Linde's Self-reproducing Inflationary Multiverse model. In Linde's model, the physical laws and constants that govern our universe adopt other values in other universes, due to variable Higgs fields. While the physics in our universe allow for the advent of life and consciousness, the physics necessary for life are not likely to exist in other universes -- Linde demonstrates this through a kind of Darwinism for universes. Our universe, then, is unique. But what are the physical laws and constants that make our universe what it is? Craig Hogan identifies five physical constants that are not bound by symmetry. Fine-tuning these constants gives rise to the basic behavior and structures of the universe. Three of the non-symmetric constants are fermion masses: the up quark mass, the down quark mass, and the electron mass. I will explore Linde's and Hogan's works by comparing the amount of uncertainty in quark masses, as calculated from the Heisenberg Uncertainty Principle, to the range of quark mass values consistent with our observed universe. Should the fine-tuning of the up quark and down quark masses be greater than the range of Heisenberg uncertainties in their respective masses (as I predict, due to quantum tunneling), then perhaps there is a correlation between the measured Heisenberg uncertainty in quark masses and the fine-tuning of masses required for our universe to be as it is. Hogan; "Why the Universe is Just So;" Reviews of Modern Physics; Issue 4; Vol. 72; pg. 1149-1161; Oct. 2000 Linde, "The Self-Reproducing Inflationary Universe;" Scientific American; No. 5; Vol. 271; pg. 48-55; Nov. 1994
Extension of Lieb-Schupp theorem to Heisenberg models with higher-order interactions
NASA Astrophysics Data System (ADS)
Tanaka, Kengo
2016-10-01
We extend the Lieb-Schupp theorem to Heisenberg models with higher-order interactions on nonfrustrated or frustrated finite lattices. These lattices are constructed by even-numbered rings with or without crossing bonds and have reflection symmetry. The results show that the ground state has total spin zero in wide interaction parameter regions which are not covered by the results of Marshall-Lieb-Mattis-type arguments.
A discussion on the Heisenberg uncertainty principle from the perspective of special relativity
NASA Astrophysics Data System (ADS)
Nanni, Luca
2016-09-01
In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for propagating statistical errors, we prove that the uncertainty relations between the moduli of conjugate observables are not relativistically invariant. The new relationships show that, in experiments involving relativistic particles, limitations of the precision of a quantity obtained by indirect calculations may affect the final result.
Genome wide expression profiling of angiogenic signaling and the Heisenberg uncertainty principle.
Huber, Peter E; Hauser, Kai; Abdollahi, Amir
2004-11-01
Genome wide DNA expression profiling coupled with antibody array experiments using endostatin to probe the angiogenic signaling network in human endothelial cells were performed. The results reveal constraints on the measuring process that are of a similar kind as those implied by the uncertainty principle of quantum mechanics as described by Werner Heisenberg. We describe this analogy and argue for its heuristic utility in the conceptualization of angiogenesis as an important step in tumor formation.
The Krichever map, vector bundles over algebraic curves, and Heisenberg algebras
NASA Astrophysics Data System (ADS)
Adams, M. R.; Bergvelt, M. J.
1993-06-01
We study the Grassmannian Gr {/x n } consisting of equivalence classes of rank n algebraic vector bundles over a Riemann surface X with an holomorphic trivialization at a fixed point p. Commutative subalgebras of gl(n, H λ), H λ being the ring of functions holomorphic on a punctured disc about p, define flows on the Grassmannian, giving rise to classes of solutions to multi-component KP hierarchies. These commutative subalgebras correspond to Heisenberg algebras in the Kac-Moody algebra associated to gl(n, H λ). One can obtain, by the Krichever map, points of Gr {/x n } (and solutions of mcKP) from coverings f: Y→X and other geometric data. Conversely for every point of Gr {/x n } and for every choice of Heisenberg algebra we construct, using the cotangent bundle of Gr {/x n }, an algebraic curve covering X and other data, thus inverting the Krichever map. We show the explicit relation between the choice of Heisenberg algebra and the geometry of the covering space.
Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins
NASA Astrophysics Data System (ADS)
Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain
2015-03-01
We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).
Ba2Cu2Te2P2O13: A new telluro-phosphate with S=1/2 Heisenberg chain
NASA Astrophysics Data System (ADS)
Xia, Mingjun; Shen, Shipeng; Lu, Jun; Sun, Young; Li, R. K.
2015-10-01
A new telluro-phosphate compound Ba2Cu2Te2P2O13 with S=1/2 Heisenberg chain has been successfully synthesized by solid state reaction and grown by flux method. Single crystal X-ray diffraction reveals that Ba2Cu2Te2P2O13 crystallizes into a monoclinic space group C2/c and cell parameters of a=17.647(3) Å, b=7.255(2) Å, c=9.191(2) Å and β=100.16 (3)°. In the structure of Ba2Cu2Te2P2O13, one dimensional [CuTePO7]3- chains are formed by tetrahedral PO4 and trigonal bi-pyramidal TeO4 joining square planar CuO4 groups. Those [CuTePO7]3- chains are inter-connected by sharing one oxygen atom from the TeO4 group to form two dimensional layers. Magnetic susceptibility and specific heat measurements confirm that the title compound is a model one dimensional Heisenberg antiferromagnetic chain system.
NASA Astrophysics Data System (ADS)
Sun, Fadi; Ye, Jinwu; Liu, Wu-Ming
2016-07-01
In this paper, we study the rotated ferromagnetic Heisenberg model (RFHM) in two different transverse fields, hx and hz, which can be intuitively visualized as studying spin-orbit coupling (SOC) effects in two-dimensional (2D) Ising or anisotropic X Y model in a transverse field. At a special SOC class, it was found in our previous work [Phys. Rev. A 92, 043609 (2015), 10.1103/PhysRevA.92.043609] that the RFHM at a zero field owns an exact spin-orbit coupled ground state called the Y -x state. It supports not only the commensurate magnons (called C -C0 and C -Cπ ), but also the incommensurate magnons (called C-IC). These magnons are nonrelativistic, not embedded in the exact ground state, so need to be thermally excited or generated by various external probes. Their dramatic response under a longitudinal hy field was recently worked out by Sun et al. [arXiv:1502.05338]. Here we find they respond very differently under the two transverse fields. Any hx (hz) introduces quantum fluctuations to the ground state and changes the collinear Y -x state to a canted coplanar Y X -x (Y Z -x ) state. The C -C0,C -Cπ , and C-IC magnons become relativistic and sneak into the quantum ground state. We determine the competing boundaries among the C -C0,C -Cπ , and C-IC magnons, especially the detailed dispersions of the C-IC magnons inside the canted phases, which can be mapped out by the transverse spin structure factors. As hx (hz) increases further, the C -C0 magnons always win the competition and emerge as the seeds to drive a transition from the Y X -x (or Y Z -x ) to the ferromagnetic along the X (orZ ) direction called the X -FM (or Z -FM) phase. We show that the transition is in the 3D Ising universality class and it becomes the 3D X Y transition at the two Abelian points. We evaluate these magnons' contributions to magnetization and specific heat at low temperatures which can be measured by various established experimental techniques. The nature of the finite
NASA Astrophysics Data System (ADS)
Rojas, Onofre; Strečka, J.; de Souza, S. M.
2016-11-01
The spin-1/2 Ising-Heisenberg two-leg ladder accounting for alternating Ising and Heisenberg inter-leg couplings in addition to the Ising intra-leg coupling is rigorously mapped onto to a mixed spin-(3/2,1/2) Ising-Heisenberg diamond chain with the nodal Ising spins S = 3 / 2 and the interstitial spin-1/2 Heisenberg dimers. The latter effective model with higher-order interactions between the nodal and interstitial spins is subsequently exactly solved within the transfer-matrix method. The model under investigation exhibits five different ground states: ferromagnetic, antiferromagnetic, superantiferromagnetic and two types of frustrated ground states with a non-zero residual entropy. A detailed study of thermodynamic properties reveals an anomalous specific-heat peak at low enough temperatures, which is strongly reminiscent because of its extraordinary height and sharpness to an anomaly accompanying a phase transition. It is convincingly evidenced, however, that the anomalous peak in the specific heat is finite and it comes from vigorous thermal excitations from a two-fold degenerate ground state towards a macroscopically degenerate excited state. Thermal entanglement between the nearest-neighbor Heisenberg spins is also comprehensively explored by taking advantage of the concurrence. The threshold temperature delimiting a boundary between the entangled and disentangled parameter space may show presence of a peculiar temperature reentrance.
NASA Astrophysics Data System (ADS)
Belgiorno, Francesco; Cacciatori, Sergio L.; Dalla Piazza, Francesco; Doronzo, Michele
2016-06-01
We investigate the quantisation in the Heisenberg representation of a model which represents a simplification of the Hopfield model for dielectric media, where the electromagnetic field is replaced by a scalar field φ and the role of the polarisation field is played by a further scalar field ψ . The model, which is quadratic in the fields, is still characterised by a non-trivial physical content, as the physical particles correspond to the polaritons of the standard Hopfield model of condensed matter physics. Causality is also taken into account and a discussion of the standard interaction representation is also considered.
Phase diagrams of a classical two-dimensional Heisenberg antiferromagnet with single-ion anisotropy
NASA Astrophysics Data System (ADS)
Leidl, R.; Selke, W.
2004-11-01
A classical variant of the two-dimensional anisotropic Heisenberg model reproducing inelastic neutron scattering experiments on La5Ca9Cu24O41 [M. Matsuda , Phys. Rev. B 68, 060406(R) (2003)] is analyzed using mostly Monte Carlo techniques. Phase diagrams with external fields parallel and perpendicular to the easy axis of the anisotropic interactions are determined, including antiferromagnetic and spin-flop phases. Mobile spinless defects, or holes, are found to form stripes which bunch, debunch, and break up at a phase transition. A parallel field can lead to a spin-flop phase.
Li, W. C.; Song, X.; Feng, J. J.; Zeng, M.; Gao, X. S.; Qin, M. H.; Jia, X. T.
2015-07-07
In this work, the effects of the random exchange interaction on the phase transitions and phase diagrams of classical frustrated Heisenberg model are investigated by Monte Carlo simulation in order to simulate the chemical doping effect in real materials. It is observed that the antiferromagnetic transitions shift toward low temperature with the increasing magnitude of the random exchange interaction, which can be qualitatively understood from the competitions among local spin states. This study is related to the magnetic properties in the doped iron-based superconductors.
Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in two dimensions
NASA Technical Reports Server (NTRS)
Dagotto, Elbio; Moreo, Adriana
1989-01-01
A Lanczos technique is used to study the frustrated spin-1/2 Heisenberg model on square lattices of 16 and 20 sites. Frustration is introduced by an interaction along the diagonals of the plaquettes with coupling J2 greater than or equal to 0. For large J2, the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of J2, the squares of order parameters associated with spin-Peierls and 'twisted'states have a peak, while a similar quantity for a chiral state shows no interesting structure.
NASA Astrophysics Data System (ADS)
Vladimirov, A. A.; Ihle, D.; Plakida, N. M.
2015-02-01
The spin-wave excitation spectrum, magnetization, and Néel temperature for the quasi-two-dimensional spin-1/2 antiferromagnetic Heisenberg model with the compass-model interaction in the plane proposed for iridates are calculated in the random phase approximation. The spin-wave spectrum agrees well with data of Lanczos diagonalization. We find that the Néel temperature is enhanced by the compass-model interaction and is close to the experimental value for Ba2IrO4.
Spin-Lattice-Coupled Order in Heisenberg Antiferromagnets on the Pyrochlore Lattice.
Aoyama, Kazushi; Kawamura, Hikaru
2016-06-24
Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at the stronger SLC is cubic symmetric characterized by the magnetic (1/2,1/2,1/2) Bragg peaks, while that at the weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local lattice distortions. Experimental implications to chromium spinels are discussed. PMID:27391746
Chiral spin liquid in the extended Heisenberg model on the Kagome lattice
NASA Astrophysics Data System (ADS)
Hu, Wenjun; Zhu, Wei; Zhang, Yi; Gong, Shoushu; Becca, Federico; Sheng, Dongning; Donna Sheng Team
2015-03-01
We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with C = 1 / 2 fractionalized Chern number.
Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain
NASA Astrophysics Data System (ADS)
Chen, Tao; Shan, Chuanjia; Li, Jinxing; Liu, Tangkun; Huang, Yanxia; Li, Hong
2010-07-01
This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.
Emergent Interacting Spin Islands in a Depleted Strong-Leg Heisenberg Ladder
NASA Astrophysics Data System (ADS)
Schmidiger, D.; Povarov, K. Yu.; Galeski, S.; Reynolds, N.; Bewley, R.; Guidi, T.; Ollivier, J.; Zheludev, A.
2016-06-01
Properties of the depleted Heisenberg spin ladder material series (C7 H10 N )2Cu1 -zZnz Br4 have been studied by the combination of magnetic measurements and neutron spectroscopy. Disorder-induced degrees of freedom lead to a specific magnetic response, described in terms of emergent strongly interacting "spin island" objects. The structure and dynamics of the spin islands is studied by high-resolution inelastic neutron scattering. This allows us to determine their spatial shape and to observe their mutual interactions, manifested by strong spectral in-gap contributions.
Emergent Interacting Spin Islands in a Depleted Strong-Leg Heisenberg Ladder.
Schmidiger, D; Povarov, K Yu; Galeski, S; Reynolds, N; Bewley, R; Guidi, T; Ollivier, J; Zheludev, A
2016-06-24
Properties of the depleted Heisenberg spin ladder material series (C_{7}H_{10}N)_{2}Cu_{1-z}Zn_{z}Br_{4} have been studied by the combination of magnetic measurements and neutron spectroscopy. Disorder-induced degrees of freedom lead to a specific magnetic response, described in terms of emergent strongly interacting "spin island" objects. The structure and dynamics of the spin islands is studied by high-resolution inelastic neutron scattering. This allows us to determine their spatial shape and to observe their mutual interactions, manifested by strong spectral in-gap contributions. PMID:27391748
Heisenberg-Limited Qubit Read-Out with Two-Mode Squeezed Light.
Didier, Nicolas; Kamal, Archana; Oliver, William D; Blais, Alexandre; Clerk, Aashish A
2015-08-28
We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, it is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics. PMID:26371653
A Numerical Study of Entanglement Entropy of the Heisenberg Model on a Bethe Cluster
NASA Astrophysics Data System (ADS)
Friedman, Barry; Levine, Greg
Numerical evidence is presented for a nearest neighbor Heisenberg spin model on a Bethe cluster, that by bisecting the cluster, the generalized Renyi entropy scales as the number of sites in the cluster. This disagrees with spin wave calculations and a naive application of the area law but agrees with previous results for non interacting fermions on the Bethe cluster. It seems this scaling is not an artifact of non interacting particles. As a consequence, the area law in greater then one dimension is more subtle then generally thought and applications of the density matrix renormalization group to Bethe clusters face difficulties at least as a matter of principle.
A quaternionic map for the steady states of the Heisenberg spin-chain
NASA Astrophysics Data System (ADS)
Mehta, Mitaxi P.; Dutta, Souvik; Tiwari, Shubhanshu
2014-01-01
We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
NASA Astrophysics Data System (ADS)
Belliard, Samuel; Crampé, Nicolas
2013-11-01
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Spin-Lattice-Coupled Order in Heisenberg Antiferromagnets on the Pyrochlore Lattice
NASA Astrophysics Data System (ADS)
Aoyama, Kazushi; Kawamura, Hikaru
2016-06-01
Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at the stronger SLC is cubic symmetric characterized by the magnetic (1/2 ,1/2 ,1/2 ) Bragg peaks, while that at the weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local lattice distortions. Experimental implications to chromium spinels are discussed.
Properties of the first excited state of nonbipartite Heisenberg spin rings
NASA Astrophysics Data System (ADS)
Schnack, J.
2000-12-01
Systematic properties of the first excited state are presented for various ring sizes and spin quantum numbers which are only partly covered by the theorem of Lieb, Schultz, and Mattis. For odd ring sizes the first excited energy eigenvalue shows unexpected degeneracy and related shift quantum numbers. As a byproduct the ground state energy as well as the energy of the first excited state of infinite chains are calculated by extrapolating the properties of only a few, finite, antiferromagnetically coupled Heisenberg rings using the powerful Levin sequence acceleration method.
New Universality Class in Spin-One-Half Fibonacci Heisenberg Chains
NASA Astrophysics Data System (ADS)
Hida, Kazuo
2004-07-01
Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.
New universality class in spin-one-half Fibonacci Heisenberg chains.
Hida, Kazuo
2004-07-16
Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity. PMID:15323863
NASA Astrophysics Data System (ADS)
Nakano, Hiroki; Hasegawa, Yasumasa; Sakai, Tôru
2015-11-01
We study the magnetization process of the spin-1/2 Heisenberg antiferromagnet on a distorted square-kagome lattice by the numerical-diagonalization method. The magnetization jump at one-third of the height of the saturation is examined in detail; we find that the jump becomes larger when a small distortion is switched on and that it is accompanied by an abrupt change in lines along microscopic spin directions. Our finite-size results successfully confirm that the magnetization jump in a spin-isotropic system is a macroscopic jump that survives in the thermodynamic limit and that the changes in spin directions are common to a spin-flop phenomenon observed in spin-anisotropic systems.
Persistent atomic spin squeezing at the Heisenberg limit
NASA Astrophysics Data System (ADS)
Wu, Ling-Na; Tey, Meng Khoon; You, Li
2016-05-01
One-axis twisting (OAT) and two-axis counter twisting (TACT) are two widely discussed processes capable of dynamically generating spin squeezed states, which have potential applications to precision measurement and entanglement detection. TACT provides better spin squeezing (SS), but has not been demonstrated as its form of interaction does not occur naturally in known physical systems. Several proposals for realizing effective TACT transformed from OAT require stringent experimental conditions, in order to overcome the problems of non-stationary (oscillating) SS and continuously varying mean spin direction. We report a simple protocol that solves both problems by freezing SS at an optimal point and realizing effectively persistent SS by inhibiting further squeezing dynamics. Explicit procedures are outlined which favorably relax experimental demands and significantly brighten the prospects for realizing TACT.
Stapp`s quantum dualism: The James/Heisenberg model of consciousness
Noyes, H.P.
1994-02-18
Henry Stapp attempts to resolve the Cartesian dilemma by introducing what the author would characterize as an ontological dualism between mind and matter. His model for mind comes from William James` description of conscious events and for matter from Werner Heisenberg`s ontological model for quantum events (wave function collapse). His demonstration of the isomorphism between the two types of events is successful, but in the author`s opinion fails to establish a monistic, scientific theory. The author traces Stapp`s failure to his adamant rejection of arbitrariness, or `randomness`. This makes it impossible for him (or for Bohr and Pauli before him) to understand the power of Darwin`s explanation of biology, let along the triumphs of modern `neo-Darwinism`. The author notes that the point at issue is a modern version of the unresolved opposition between Leucippus and Democritus on one side and Epicurus on the other. Stapp`s views are contrasted with recent discussions of consciousness by two eminent biologists: Crick and Edelman. They locate the problem firmly in the context of natural selection on the surface of the earth. Their approaches provide a sound basis for further scientific work. The author briefly examines the connection between this scientific (rather than ontological) framework and the new fundamental theory based on bit-strings and the combinatorial hierarchy.
Spontaneous plaquette dimerization in the J_1-J2 Heisenberg model
NASA Astrophysics Data System (ADS)
Capriotti, Luca; Sorella, Sandro
2000-03-01
The nature of the non magnetic phases of a quantum antiferromagnet is a topic of great interest and has been a subject of intense theoretical investigation since Anderson's suggestion [1] about the possible connections with the mechanism of high-Tc superconductivity. Within the Heisenberg model the simplest way in which the antiferromagnetism can be destabilized is by introducing a next-nearest-neighbor frustrating interaction leading to the so called J_1-J2 Hamiltonian. We have investigated the zero temperature properties the spin-half J_1-J2 Heisenberg antiferromagnet on the square lattice using exact diagonalization and the recently developed Green Function Monte Carlo with Stochastic Reconfiguration technique [2]. The spin gap and the susceptibilities for the most important crystal symmetry breaking operators have been computed. A genuine and somehow unexpected ``plaquette RVB'', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for J_2/J1 ~= 0.5 [3]. ^1 P. W. Anderson, Science 235, 1196 (1987). ^2 S. Sorella, Phys. Rev. Lett. 80, 4558 (1998); S. Sorella and L. Capriotti, Phys. Rev. B (in press). ^3 L. Capriotti and S. Sorella, cond-mat/9911161
NASA Astrophysics Data System (ADS)
Xiang, Ying; Chen, Yuan; Chen, Qi-Zhou; Zhang, Jun; Liu, Yi-Kun
2008-12-01
The effect of magnetic field h on the longitudinal susceptibility in a spin S=1/2 exchange anisotropic three-dimensional Heisenberg antiferromagnet, is studied by the double-time Green's function method within Tyablikov approximation. The calculation results indicated that the height χ(Tm) and position Tm of the maximum of the longitudinal susceptibility display different behaviors related to the magnetic fields and exchange anisotropic parameters. These behaviors are very different from that in the exchange anisotropic Heisenberg ferromagnet in the magnetic field. The results are: (1) When the field h is weak, in a antiferromagnet, the height χ(Tm) is a constant χ0 which is independent of field and exchange anisotropy, but the position Tm is only a function of the exchange anisotropy. While in a ferromagnet, both χ(Tm) and Tm are a function of field and the exchange anisotropy. (2) When the field h is strong, in a antiferromagnet, χ(Tm) becomes dependent of field and the exchange anisotropy, and χ(Tm) and Tm are fitted satisfactory to power laws: χ(Tm)-χ0∝hd and TN-Tm∝hc, respectively. Here TN is the Neel temperature. On the contrary, in a ferromagnet, χ(Tm) and Tm are fitted to power laws: χ(Tm)∝h and Tm-Tc∝h, where Tc is the Curie temperature. The above results are very useful in studying the magnetic property of coordination polymers.
RVB signatures in the spin dynamics of the square-lattice Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Ghioldi, E. A.; Gonzalez, M. G.; Manuel, L. O.; Trumper, A. E.
2016-03-01
We investigate the spin dynamics of the square-lattice spin-\\frac{1}{2} Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at (π,0) found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
Magnetization Process of Spin-1/2 Heisenberg Antiferromagnets on a Layered Triangular Lattice
NASA Astrophysics Data System (ADS)
Yamamoto, Daisuke; Marmorini, Giacomo; Danshita, Ippei
2016-02-01
We study the magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on a layered triangular lattice by means of a numerical cluster mean-field method with a scaling scheme (CMF+S). It has been known that antiferromagnetic spins on a two-dimensional (2D) triangular lattice with quantum fluctuations exhibit a one-third magnetization plateau in the magnetization curve under magnetic field. We demonstrate that the CMF+S quantitatively reproduces the magnetization curve including the stabilization of the plateau. We also discuss the effects of a finite interlayer coupling, which is unavoidable in real quasi-2D materials. It has been recently argued for a model of the layered-triangular-lattice compound Ba3CoSb2O9 that such interlayer coupling can induce an additional first-order transition at a strong field. We present the detailed CMF+S results for the magnetization and susceptibility curves of the fundamental Heisenberg Hamiltonian in the presence of magnetic field and weak antiferromagnetic interlayer coupling. The extra first-order transition appears as a quite small jump in the magnetization curve and a divergence in the susceptibility at a strong magnetic field ˜0.712 of the saturation field.
Yu, Rong; Si, Qimiao
2015-09-11
Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments. PMID:26406842
NASA Astrophysics Data System (ADS)
Bishop, R. F.; Li, P. H. Y.
2016-06-01
The coupled cluster method (CCM) is employed to very high orders of approximation to study the ground-state (GS) properties of the spin-s Heisenberg antiferromagnet (with isotropic interactions, all of equal strength, between nearest-neighbour pairs only) on the honeycomb lattice. We calculate with high accuracy the complete set of GS parameters that fully describes the low-energy behaviour of the system, in terms of an effective magnon field theory, viz., the energy per spin, the magnetic order parameter (i.e., the sublattice magnetization), the spin stiffness and the zero-field (uniform, transverse) magnetic susceptibility, for all values of the spin quantum numbers in the range 1/2 ≤ s ≤ 9/2. The CCM data points are used to calculate the leading quantum corrections to the classical (s → ∞) values of these low-energy parameters, considered as large-s asymptotic expansions.
NASA Astrophysics Data System (ADS)
Kurita, Moyuru; Yamaji, Youhei; Morita, Satoshi; Imada, Masatoshi
2015-07-01
We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do not have the spin-rotational symmetry. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type projections, and quantum number projections. The generalized wave functions allow describing states including a wide class of symmetry-broken states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We detail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which imposes the conservation of not only the momentum quantum number but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency is tested for the Kitaev and Kitaev-Heisenberg models, which lack the SU(2) spin-rotational symmetry except at the Heisenberg limit. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the reach of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. An application to a closely related itinerant model described by a multiorbital Hubbard model with the spin-orbit interaction also shows promising benchmark results. The strong-coupling limit of the multiorbital Hubbard model is indeed described by the Kitaev model. Our framework offers accurate solutions for the systems where strong electron correlation and spin
Multicanonical Monte Carlo simulations of anisotropic SU(3) and SU(4) Heisenberg models
NASA Astrophysics Data System (ADS)
Harada, Kenji; Kawashima, Naoki; Troyer, Matthias
2009-03-01
We present the results of multicanonical Monte Carlo simulations on two-dimensional anisotropic SU(3) and SU(4) Heisenberg models. In our previous study [K. Harada, et al., J. Phys. Soc. Jpn. 76, 013703 (2007)], we found evidence for a direct quantum phase transition from the valence-bond-solid(VBS) phase to the SU(3) symmetry breaking phase on the SU(3) model and we proposed the possibility of deconfined critical phenomena (DCP) [T. Senthil, et al., Science 303, 1490 (2004); T. Grover and T. Senthil, Phys. Rev. Lett. 98, 247202 (2007)]. Here we will present new results with an improved algorithm, using a multicanonical Monte Carlo algorithm. Using a flow method-like technique [A.B. Kuklov, et al., Annals of Physics 321, 1602 (2006)], we discuss the possibility of DCP in both models.
Nonequilibrium behaviors of the three-dimensional Heisenberg model in the Swendsen-Wang algorithm.
Nonomura, Yoshihiko; Tomita, Yusuke
2016-01-01
Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)JUPSAU0031-901510.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies. PMID:26871018
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
NASA Technical Reports Server (NTRS)
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Magnetic order in the two-dimensional compass-Heisenberg model
NASA Astrophysics Data System (ADS)
Vladimirov, Artem A.; Ihle, Dieter; Plakida, Nikolay M.
2015-06-01
A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range order (LRO) and short-range order (SRO) at arbitrary temperatures. The magnetization, Néel temperature TN, specific heat, and uniform static spin susceptibility χ are calculated self-consistently. As the main result, we obtain LRO at finite temperatures in two dimensions, where the dependence of TN on the compass-model interaction is studied. We find that TN is close to the experimental value for Ba2IrO4. The effects of SRO are discussed in relation to the temperature dependence of χ.
Classical ground states of Heisenberg and X Y antiferromagnets on the windmill lattice
NASA Astrophysics Data System (ADS)
Jeevanesan, Bhilahari; Orth, Peter P.
2014-10-01
We investigate the classical Heisenberg and planar (X Y ) spin models on the windmill lattice. The windmill lattice is formed out of two widely occurring lattice geometries: a triangular lattice is coupled to its dual honeycomb lattice. Using a combination of iterative minimization, heat-bath Monte Carlo simulations, and analytical calculations, we determine the complete ground-state phase diagram of both models and find the exact energies of the phases. The phase diagram shows a rich phenomenology due to competing interactions and hosts, in addition to collinear and various coplanar phases, also intricate noncoplanar phases. We briefly outline different paths to an experimental realization of these spin models. Our extensive study provides a starting point for the investigation of quantum and thermal fluctuation effects.
Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
NASA Astrophysics Data System (ADS)
Fagotti, Maurizio; Collura, Mario; Essler, Fabian H. L.; Calabrese, Pasquale
2014-03-01
We consider the time evolution after quantum quenches in the spin-1/2 Heisenberg XXZ quantum spin chain with Ising-type anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including Néel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.
Sudden death of distillability in a two-qutrit anisotropic Heisenberg spin model
NASA Astrophysics Data System (ADS)
Guo, You-neng; Fang, Mao-fa; Zou, Hong-mei; Zhang, Shi-yang; Liu, Xiang
2015-06-01
Sudden death of distillability for a two-qutrit anisotropic Heisenberg XX chain with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous magnetic field is studied in detail. By using the negativity and realignment criterion, we show that certain initial prepared free entangled states may become bound entangled or separable states in a finite time. Moreover, the influences of the isotropic bilinear interaction parameter, the external magnetic field strength, the DM interaction parameter, as well as the intrinsic decoherence parameter on the possibility of distillability sudden death (DSD) have been studied. The results show, controlling the isotropic bilinear interaction parameter, the external magnetic field strength, the DM interaction parameter, as well as the intrinsic decoherence parameter, can accelerate the possibility of DSD in the present model.
NASA Astrophysics Data System (ADS)
Lima, L. S.
2016-08-01
We study the influence of the site disorder in the long range order and in the spin transport in the two-dimensional Heisenberg antiferromagnet with ion-single anisotropy, in the square lattice in T=0 using the SU(3) Schwinger boson theory. We analyze these properties in the regime of Bose-Einstein condensation, where the bosons tz are condensed:
Low-energy singlet excitations in spin-1/2 Heisenberg antiferromagnet on square lattice
NASA Astrophysics Data System (ADS)
Aktersky, A. Yu.; Syromyatnikov, A. V.
2016-05-01
We present an approach based on a dimer expansion which describes low-energy singlet excitations (singlons) in spin-1/2 Heisenberg antiferromagnet on simple square lattice. An operator ("effective Hamiltonian") is constructed whose eigenvalues give the singlon spectrum. The "effective Hamiltonian" looks like a Hamiltonian of a spin-1/2 magnet in strong external magnetic field and it has a gapped spectrum. It is found that singlet states lie above triplet ones (magnons) in the whole Brillouin zone except in the vicinity of the point (π , 0), where their energies are slightly smaller. Based on this finding, we suggest that a magnon decay is possible near (π , 0) into another magnon and a singlon which may contribute to the dip of the magnon spectrum near (π , 0) and reduce the magnon lifetime. It is pointed out that the singlon-magnon continuum may contribute to the continuum of excitations observed recently near (π , 0).
Absence of Néel order in Heisenberg chains: Long-range antiferromagnetic interactions
NASA Astrophysics Data System (ADS)
Pacobahyba, J. T.; Nunes, Wagner; de Sousa, J. Ricardo
2004-03-01
We have studied the Heisenberg chain with long-range antiferromagnetic interactions proportional to (-1)n/np (n=1,2,…,∞) by the method of a double-time-temperature Green’s function within Tyablikov’s decoupling approximation. Using the two-sublattice approach developed by Hewson and ter Haar, and solving the equation of motion for the Green’s function, we obtain the Néel temperature TN as a function of p. We have conjectured that for all p>1 the present approach predicts orientational disorder at all finite temperatures (i.e., TN=0). Our results are in accordance with spin-wave arguments and disagreement with renormalization group that predicts a phase transition at p≃1.85 at T=0.
Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Nataf, Pierre; Lajkó, Miklós; Corboz, Philippe; Läuchli, Andreas M.; Penc, Karlo; Mila, Frédéric
2016-05-01
We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011), 10.1103/PhysRevA.84.011611]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.
Werner states and the two-spinors Heisenberg anti-ferromagnet
NASA Astrophysics Data System (ADS)
Batle, J.; Casas, M.; Plastino, A.; Plastino, A. R.
2005-08-01
We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. 87 (2001) 017901] and using the statistical tool called entropic non-triviality [P.W. Lamberti, M.T. Martin, A. Plastino, O.A. Rosso, Physica A 334 (2004) 119], that there is a one-to-one correspondence between (i) the mixing coefficient x of a Werner state, on the one hand, and (ii) the temperature T of the one-dimensional Heisenberg two-spin chain with a magnetic field B along the z-axis, on the other one. This is true for each value of B below a certain critical value B. The pertinent mapping depends on the particular B-value one selects within such a range.
Solving the {eta}-problem in hybrid inflation with Heisenberg symmetry and stabilized modulus
Antusch, Stefan; Dutta, Koushik; Kostka, Philipp M.; Bastero-Gil, Mar; King, Steve F. E-mail: mbg@ugr.es E-mail: sfk@hep.phys.soton.ac.uk
2009-01-15
We propose a class of models in which the {eta}-problem of supersymmetric hybrid inflation is resolved using a Heisenberg symmetry, where the associated modulus field is stabilized and made heavy with the help of the large vacuum energy during inflation without any fine-tuning. The proposed class of models is well motivated both from string theory considerations, since it includes the commonly encountered case of no-scale supergravity Kaehler potential, and from the perspective of particle physics since a natural candidate for the inflaton in this class of models is the right-handed sneutrino which is massless during the inflationary epoch, and subsequently acquires a large mass at the end of inflation. We study a specific example motivated by sneutrino hybrid inflation with no-scale supergravity in some detail, and show that the spectral index may lie within the latest WMAP range, while the tensor-to-scalar ratio is very small.
A note for Riesz transforms associated with Schrödinger operators on the Heisenberg Group
NASA Astrophysics Data System (ADS)
Liu, Yu; Tang, Guobin
2016-03-01
Let {{H}^n} be the Heisenberg group and Q=2n+2 be its homogeneous dimension. The Schrödinger operator is denoted by - {Δ _{{{H}^n}}} + V , where {Δ _{{{H}^n}}} is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class {B_{{q_1}}} for {q_1} ≥ Q/2 . Let H^p_L({H}^n) be the Hardy space associated with the Schrödinger operator for Q/Q+δ _0
Scaling behavior of spin gap of the bond alternating anisotropic spin-1/2 Heisenberg chain
NASA Astrophysics Data System (ADS)
Paul, Susobhan; Ghosh, Asim Kumar
2016-05-01
Scaling behavior of spin gap of a bond alternating spin-1/2 anisotropic Heisenberg chain has been studied both in ferromagnetic (FM) and antiferromagnetic (AFM) cases. Spin gap has been estimated by using exact diagonalization technique. All those quantities have been obtained for a region of anisotropic parameter Δ defined by 0≤Δ≤1. Spin gap is found to develop as soon as the non-uniformity in the alternating bond strength is introduced in the AFM regime which furthermore sustains in the FM regime as well. Scaling behavior of the spin gap has been studied by introducing scaling exponent. The variation of scaling exponents with Δ is fitted with a regular function.
NASA Astrophysics Data System (ADS)
Lima, L. S.
2016-07-01
We use the SU(3) Schwinger's boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents a single-ion anisotropy and J1 and J2 exchange interactions. We study the spin transport in the Bose-Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid:
NASA Astrophysics Data System (ADS)
Ueda, Hiroshi; Kusakabe, Koichi
2012-02-01
Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain with boundary S/2 spins coupling antiferromagnetically (Jend> 0) is analyzed by use of the non-Abelian DMRG method. The Haldane gap δ, the magnon velocity v, the inter-magnon scattering length a, and the scattering length ab of the boundary coupling are evaluated. The length ab, which represents the contribution of boundary effects, depends on Jend drastically, while δ, v, and a are constant irrespective of Jend. Our method estimates the gap of the S=2 AF chain as δ= 0.0891623(9) using a chain length up to 2048, which is longer than the correlation length.
Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
NASA Astrophysics Data System (ADS)
Choi, Seongsoo; Kim, Woohyun; Kim, Jongho
2016-09-01
We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits ) of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: N/spins!M ! (N spins-M ) ! >Norbits ) of the spin-1/2 Heisenberg antiferromagnet on the L ×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square) for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
NASA Astrophysics Data System (ADS)
Luban, Marshall; Modler, Robert; Axenovich, Maria; Canfield, Paul; Bud'Ko, Sergey; Schröder, Christian; Schnack, Jürgen; Müller, Achim; Kögerler, Paul; Harrison, Neil
2001-03-01
The Keplerate species Mo_72Fe_30 containing 30 high-spin Fe^3+ ions, is by far the largest paramagnetic molecule synthesized to date, and it serves as an effective building block and prototype for a new class of diverse molybdenum-oxygen based compounds. These substances are of importance for identifying the most pertinent criteria for the passage from microscopic to macroscopic magnetism, and for their potential as molecular-based electronic and magnetic devices. We report excellent agreement, from room temperature down to 0.1 K, and for magnetic fields up to 60 Tesla between our theoretical results based on the classical Heisenberg model and our measurements of its magnetic properties.
Low-temperature magnetic measurements of an [ital S]=1 linear-chain Heisenberg antiferromagnet
Avenel, O.; Xu, J.; Xia, J.S.; Xu, M.; Andraka, B.; Lang, T.; Moyland, P.L.; Ni, W.; Signore, P.J.C.; van Woerkens, C.M.C.M.; Adams, E.D.; Ihas, G.G.; Meisel, M.W.; Nagler, S.E.; Sullivan, N.S.; Takano, Y. ); Talham, D.R. ); Goto, T. ); Fujiwara, N. )
1992-10-01
The temperature-dependent magnetic susceptibility, [chi]([ital T]), of two pure samples of the [ital S]=1 linear-chain Heisenberg antiferromagnet Ni(C[sub 2]H[sub 8]N[sub 2])[sub 2]NO[sub 2](ClO[sub 4]), commonly known as NENP, has been measured from approximately 300 K to 300 [mu]K. Our measurements of [chi]([ital T]) are in agreement with existing results of other researchers who worked above 1.2 K. Below 1.2 K, [chi]([ital T]) increases with decreasing temperature. The results suggest that the low-temperature increase of [chi]([ital T]) is not a consequence of a single source of paramagnetic impurities in the samples but may arise from [ital S]=1/2 end-chain interactions.
Partition function zeros and magnetization plateaus of the spin-1 Ising-Heisenberg diamond chain
NASA Astrophysics Data System (ADS)
Hovhannisyan, V. V.; Ananikian, N. S.; Kenna, R.
2016-07-01
We study the properties of the generalized spin-1 Ising-Heisenberg model on a diamond chain, which can be considered as a theoretical model for the homometallic magnetic complex [Ni3(C4H2O4)2 -(μ3 - OH) 2(H2O)4 ] n ṡ(2H2 O) n. The model possesses a large variety of ground-state phases due to the presence of biquadratic and single-ion anisotropy parameters. Magnetization and quadrupole moment plateaus are observed at one- and two-thirds of the saturation value. The distributions of Yang-Lee and Fisher zeros are studied numerically for a variety of values of the model parameters. The usual value σ = -1/2 alongside an unusual value σ = -2/3 is determined for the Yang-Lee edge singularity exponents.
Heisenberg behavior of some carbon-beryllium compounds: How well truncated-CI approaches work.
Calzado, Carmen J; Monari, A; Evangelisti, S
2011-01-30
This works tries to establish the performance of truncated CI calculations on the evaluation of magnetic coupling parameters with respect to available FCI estimates on a set of carbon-beryllium clusters. First-, second- and third-neighbor magnetic coupling constants have been evaluated and many body effective parameters as the cyclic terms. They result from the fitting of the low-lying states to the eigenvalues of an extended Heisenberg Hamiltonian, involving not only two-body isotropic terms but also cyclic terms. SDCI and DDCI calculations have been carried out and their performance compared with FCI ones. The impact of the basis set choice and size-consistency errors have been explored.
NASA Astrophysics Data System (ADS)
Ward, B. F. L.
2015-10-01
We argue that our recent success in using our resummed quantum gravity (RQG) approach to Einstein’s general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the cosmological constant Λ supports the use of quantum mechanical consistency requirements to constrain the main uncertainty in that very promising result. This main uncertainty, which is due to the uncertainty in the value of the time ttr at which the transition from the Planck scale cosmology to the FRW model occurs, is shown to be reduced, by requiring consistency between the Heisenberg uncertainty principle and the known properties of the solutions of Einstein’s equations, from four orders of magnitude to the level of a factor of 𝒪(10). This lends more credibility to the overall RQG approach itself, in general, and to our estimate of Λ in particular.
Putz, Mihai V.
2010-01-01
Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor 1-n2, in terms of magnitude n∈[0,1]. of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function. PMID:21152325
Enhancing the Trace Norm and Bures Norm Measurement-Induced Nonlocality in the Heisenberg XYZ Model
NASA Astrophysics Data System (ADS)
Xie, Yu-Xia; Liu, Jing; Ma, Hong
2016-07-01
Nonlocality is one unique characteristic of quantum mechanics and an essential resource for quantum communication and computation. We investigate two measures of the well-defined geometric measurement-induced nonlocality (MIN) in the Heisenberg XYZ model, and found that considerable enhancement of the MINs can be achieved by tuning strength of the anisotropic parameter, the J z coupling, and the Dzyaloshinsky-Moriya (DM) interaction of the model. Particularly, the maxima of the two MINs can be obtained when the strength of the J z coupling or the DM interaction approaches infinity. We have also demonstrated the singular behaviors of the two MINs such as the nonunique states ordering and the sudden change behaviors.
Cat-states in the framework of Wigner-Heisenberg algebra
NASA Astrophysics Data System (ADS)
Dehghani, A.; Mojaveri, B.; Shirin, S.; Saedi, M.
2015-11-01
A one-parameter generalized Wigner-Heisenberg algebra (WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule [ x ˆ ,pˆλ ] = i(1 + 2 λ R ˆ) and also highlights the dynamical symmetries of the pseudo-harmonic oscillator (PHO). The present article is devoted to the study of new cat-states built from λ-deformed Schrödinger coherent states, which according to the Barut-Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states are obtained. Nonclassical features and quantum statistical properties of these states are studied by evaluation of Mandel's parameter and quadrature squeezing with respect to the λ-deformed canonical pairs (x ˆ ,pˆλ) . It is shown that these states minimize the uncertainty relations of each pair of the su(1 , 1) components.
Putz, Mihai V
2010-01-01
Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor 1-n2, in terms of magnitude n∈[0,1]. of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function.
Nonequilibrium behaviors of the three-dimensional Heisenberg model in the Swendsen-Wang algorithm
NASA Astrophysics Data System (ADS)
Nonomura, Yoshihiko; Tomita, Yusuke
2016-01-01
Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014), 10.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D X Y model. The critical exponents evaluated in the present study are consistent with those in previous studies.
EuCo2P2 : A model molecular-field helical Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Sangeetha, N. S.; Cuervo-Reyes, Eduardo; Pandey, Abhishek; Johnston, D. C.
2016-07-01
The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins-7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN=66.5 K with the helix axis along the c axis and with the ordered moments aligned within the a b plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization, and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility χ , high-field magnetization, and magnetic heat capacity of EuCo2P2 single crystals at temperature T ≤TN with the predictions of our recent formulation of molecular-field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ˜T3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2 , respectively. These values are enhanced by a factor of ˜2.5 above those found from DFT electronic structure calculations for the two compounds. The calculations also find ferromagnetic Eu-Eu exchange interactions within the a b plane and AFM interactions between Eu spins in nearest- and next-nearest planes, in agreement with the MFT analysis of χa b(T ≤TN) .
EuCo2P2: A Model Molecular-Field Helical Heisenberg Antiferromagnet
Sangeetha, N. S.; Cuervo-Reyes, Eduardo; Pandey, Abhishek; Johnston, D. C.
2016-07-19
The metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins-7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN=66.5 K with the helix axis along the c axis and with the ordered moments aligned within the ab plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization, and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility χ, high-field magnetization, and magnetic heat capacity of EuCo2P2 single crystals at temperature T≤TNmore » with the predictions of our recent formulation of molecular-field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ~T3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2, respectively. These values are enhanced by a factor of ~2.5 above those found from DFT electronic structure calculations for the two compounds. Additionally, the calculations also find ferromagnetic Eu–Eu exchange interactions within the ab plane and AFM interactions between Eu spins in nearest- and next-nearest planes, in agreement with the MFT analysis of χab(T≤TN).« less
NASA Astrophysics Data System (ADS)
Thesberg, Mischa; Sørensen, Erik S.
2014-10-01
Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J‧ - J2 plane of this model, which connects the J1 - J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1 - J2 chain (J‧ = 0) are found to extend into the J‧ - J2 plane and connect with points on the J2 = 0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ120\\circ , χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J‧, J2 ≪ J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1 - J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.
EuCo2P2: A model molecular-field helical Heisenberg antiferromagnet
Sangeetha, N. S.; Cuervo-Reyes, Eduardo; Pandey, Abhishek; Johnston, D. C.
2016-07-19
Here, the metallic compound EuCo2P2 with the body-centered tetragonal ThCr2Si2 structure containing Eu spins-7/2 was previously shown from single-crystal neutron diffraction measurements to exhibit a helical antiferromagnetic (AFM) structure below TN=66.5 K with the helix axis along the c axis and with the ordered moments aligned within the ab plane. Here we report crystallography, electrical resistivity, heat capacity, magnetization, and magnetic susceptibility measurements on single crystals of this compound. We demonstrate that EuCo2P2 is a model molecular-field helical Heisenberg antiferromagnet from comparisons of the anisotropic magnetic susceptibility χ, high-field magnetization, and magnetic heat capacity of EuCo2P2 single crystals at temperaturemore » T ≤ TN with the predictions of our recent formulation of molecular-field theory. Values of the Heisenberg exchange interactions between the Eu spins are derived from the data. The low-T magnetic heat capacity ~T3 arising from spin-wave excitations with no anisotropy gap is calculated and found to be comparable to the lattice heat capacity. The density of states at the Fermi energy of EuCo2P2 and the related compound BaCo2P2 are found from the heat capacity data to be large, 10 and 16 states/eV per formula unit for EuCo2P2 and BaCo2P2, respectively. These values are enhanced by a factor of ~2.5 above those found from DFT electronic structure calculations for the two compounds. The calculations also find ferromagnetic Eu–Eu exchange interactions within the ab plane and AFM interactions between Eu spins in nearest- and next-nearest planes, in agreement with the MFT analysis of χab(T ≤ TN).« less
Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}: A new telluro-phosphate with S=1/2 Heisenberg chain
Xia, Mingjun; Shen, Shipeng; Lu, Jun; Sun, Young; Li, R.K.
2015-10-15
A new telluro-phosphate compound Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} with S=1/2 Heisenberg chain has been successfully synthesized by solid state reaction and grown by flux method. Single crystal X-ray diffraction reveals that Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} crystallizes into a monoclinic space group C2/c and cell parameters of a=17.647(3) Å, b=7.255(2) Å, c=9.191(2) Å and β=100.16 (3)°. In the structure of Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, one dimensional [CuTePO{sub 7}]{sup 3−} chains are formed by tetrahedral PO{sub 4} and trigonal bi-pyramidal TeO{sub 4} joining square planar CuO{sub 4} groups. Those [CuTePO{sub 7}]{sup 3−} chains are inter-connected by sharing one oxygen atom from the TeO{sub 4} group to form two dimensional layers. Magnetic susceptibility and specific heat measurements confirm that the title compound is a model one dimensional Heisenberg antiferromagnetic chain system. - Graphical abstract: Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, containing (CuTePO{sub 7}){sup 3−} chains formed by PO{sub 4} and TeO{sub 4} joining CuO{sub 4} groups, shows typical 1D Heisenberg antiferromagnetic chain model behavior as confirmed by magnetic measurements. - Highlights: • New telluro-phosphate Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} has been grown. • It features layered structure composed of [CuTePO{sub 7}]{sup 3−} chains and TeO{sub 4} groups. • It shows the Heisenberg antiferromagnetic chain behavior. • It is transparent in the range of 1000–2500 nm with a UV absorption edge of 393 nm.
Zhang, Guo-Feng
2007-03-15
Thermal entanglement of a two-qubit Heisenberg chain in the presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as the quantum channel are investigated. It is found that the DM interaction can excite entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of the input; its dependences on the temperature, DM interaction, and spin coupling constant are given in detail. Entanglement teleportation will be better realized via an antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of the DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of whether the spin chains are antiferromagnetic or ferromagnetic.
NASA Technical Reports Server (NTRS)
Baskaran, G.
1989-01-01
Using a nonmean-field approach the triangular-lattice S = 1/2 Heisenberg antiferromagnet with nearest- and next-nearest-neighbor couplings is shown undergo an Ising-type phase transition into a chiral-symmetry-broken phase (Kalmeyer-Laughlin-like state) at small T. Removal of next-nearest-neighbor coupling introduces a local Z2 symmetry, thereby suppressing any finite-T chiral order.
NASA Astrophysics Data System (ADS)
Brennan, Richard P.
1998-09-01
"Here is a book I wish I had when taking physics my senior year in high school!" -Book Report A lively illumination of modern physics' marquee players, featuring: * Albert Einstein * Max Planck * Ernest Rutherford * Niels Bohr * Werner Heisenberg * Richard Feynman * Murray Gell-Mann "Brennan has a knack for explaining difficult technicalities simply. His essays give a useful summary of twentieth-century science." -Financial Times "Highly recommended to expert and layperson alike." -Choice
Semiclassical theory of the magnetization process of the triangular lattice Heisenberg model
NASA Astrophysics Data System (ADS)
Coletta, Tommaso; Tóth, Tamás A.; Penc, Karlo; Mila, Frédéric
2016-08-01
Motivated by the numerous examples of 1/3 magnetization plateaux in the triangular-lattice Heisenberg antiferromagnet with spins ranging from 1/2 to 5/2, we revisit the semiclassical calculation of the magnetization curve of that model, with the aim of coming up with a simple method that allows one to calculate the full magnetization curve and not just the critical fields of the 1/3 plateau. We show that it is actually possible to calculate the magnetization curve including the first quantum corrections and the appearance of the 1/3 plateau entirely within linear spin-wave theory, with predictions for the critical fields that agree to order 1 /S with those derived a long time ago on the basis of arguments that required going beyond linear spin-wave theory. This calculation relies on the central observation that there is a kink in the semiclassical energy at the field where the classical ground state is the collinear up-up-down structure and that this kink gives rise to a locally linear behavior of the energy with the field when all semiclassical ground states are compared to each other for all fields. The magnetization curves calculated in this way for spin 1/2, 1, and 5/2 are shown to be in good agreement with available experimental data.
Magnon energy renormalization and low-temperature thermodynamics of O(3) Heisenberg ferromagnets
Radošević, Slobodan M. Pantić, Milan R.; Pavkov-Hrvojević, Milica V.; Kapor, Darko V.
2013-12-15
We present the perturbation theory for lattice magnon fields of the D-dimensional O(3) Heisenberg ferromagnet. The effective Hamiltonian for the lattice magnon fields is obtained starting from the effective Lagrangian, with two dominant contributions that describe magnon–magnon interactions identified as a usual gradient term for the unit vector field and a part originating in the Wess–Zumino–Witten term of the effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on the basis of which we investigate the influence of magnon–magnon interactions on magnon self-energy and ferromagnet free energy. We also comment appearance of spurious terms in low-temperature series for the free energy by examining magnon–magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian). -- Highlights: •Lattice magnon Hamiltonian constructed from the effective Lagrangian. •New Feynman diagrams with colored propagators and vertices for lattice scalar fields. •Influence of magnon–magnon interactions from the WZW term on magnon energies and free energy of O(3) HFM.
Spin-1/2 Heisenberg J1-J2 antiferromagnet on the kagome lattice
NASA Astrophysics Data System (ADS)
Iqbal, Yasir; Poilblanc, Didier; Becca, Federico
2015-01-01
We report variational Monte Carlo calculations for the spin-1/2 Heisenberg model on the kagome lattice in the presence of both nearest-neighbor J1 and next-nearest-neighbor J2 antiferromagnetic superexchange couplings. Our approach is based upon Gutzwiller projected fermionic states that represent a flexible tool to describe quantum spin liquids with different properties (e.g., gapless and gapped). We show that, on finite clusters, a gapped Z2 spin liquid can be stabilized in the presence of a finite J2 superexchange, with a substantial energy gain with respect to the gapless U (1 ) Dirac spin liquid. However, this energy gain vanishes in the thermodynamic limit, implying that, at least within this approach, the U (1 ) Dirac spin liquid remains stable in a relatively large region of the phase diagram. For J2/J1≳0.3 , we find that a magnetically ordered state with q =0 overcomes the magnetically disordered wave functions, suggesting the end of the putative gapless spin-liquid phase.
Magnetic phase diagram of quasi-2D quantum Heisenberg antiferromagnets with XY anisotropy
NASA Astrophysics Data System (ADS)
Xiao, Fan; Landee, Christopher; Turnbull, Mark; Fortune, Nathanael; Hannahs, Scott
2012-02-01
The magnetic phase diagram of a quasi-2D quantum Heisenberg antiferromagnetic compound Cu(pz)2(ClO4)2 [1] has been determined by experimental measurements; TN shows a strong field dependence. The data reveal the presence of a small (0.5%) amount of XY anisotropy. QMC simulations have been performed to examine the role of the anisotropy and the interlayer exchange (') upon the phase diagram [2,3]. Comparison of the QMC results with the experimental phase diagram will be presented. [4pt] [1] F. Xiao, F. M. Woodward, C. P. Landee, M. M. Turnbull, C. Mielke, N. Harrison, T. Lancaster, S. J. Blundell, P. J. Baker, P. Babkevich, and F. L. Pratt. Phys. Rev. B, 79(13): 134412 (2009) [0pt] [2] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. B, 68(6):060402 (2003). [0pt] [3] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. Lett., 90(16): 167205 (2003).
Heisenberg antiferromagnet on Cayley trees: Low-energy spectrum and even/odd site imbalance
NASA Astrophysics Data System (ADS)
Changlani, Hitesh J.; Ghosh, Shivam; Henley, Christopher L.; Läuchli, Andreas M.
2013-02-01
To understand the role of local sublattice imbalance in low-energy spectra of s=(1)/(2) quantum antiferromagnets, we study the s=(1)/(2) quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an “anomalous” singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being “giant spins” arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.
NASA Astrophysics Data System (ADS)
Wu, Ling-Na; You, L.
2016-03-01
We show that the ground state of a spin-1 atomic condensate with antiferromagnetic interactions constitutes a useful resource for quantum metrology upon approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, the antiferromagnetic ground-state condensate is a condensate of spin-singlet atom pairs. The inherent correlation between paired atoms allows for parameter estimation at precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by the scaled quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift p to spin-dependent atomic interaction c is studied. At a typical value of p =0.4 c , which corresponds to a magnetic field of 28.6 μ G for c =50 h Hz (for 23Na atom condensate in the F =1 state at a typical density of ˜1014cm-3 ), the scaled QFI can reach ˜0.48 N , which approaches the limit of 0.5 N for the twin-Fock state |N/2 > +|N/2 > - . Our work encourages experimental efforts to reach the ground state of an antiferromagnetic condensate at a extremely low magnetic field.
The ground state of a spin-1 anti-ferromagnetic atomic condensate for Heisenberg limited metrology
NASA Astrophysics Data System (ADS)
Wu, Ling-Na; You, Li
2016-05-01
The ground state of a spin-1 atomic condensate with anti-ferromagnetic interaction can be applied to quantum metrology approaching the Heisenberg limit. Unlike a ferromagnetic condensate state where individual atomic spins are aligned in the same direction, atoms in an anti-ferromagnetic ground state condensate exist as spin singlet pairs, whose inherent correlation promises metrological precisions beyond the standard quantum limit (SQL) for uncorrelated atoms. The degree of improvement over the SQL is measured by quantum Fisher information (QFI), whose dependence on the ratio of linear Zeeman shift p to spin-dependent atomic interaction c is studied. At a typical value of p = 0 . 4 c corresponding to a magnetic field of 28 . 6 μ G with c = h × 50 Hz (for 23 Na atom condensate in the F = 1 state at a typical density of ~1014cm-3), the scaled QFI can reach ~ 0 . 48 N , which is close to the limits of N for NooN state, or 0 . 5 N for twin-Fock state. We hope our work will stimulate experimental efforts towards reaching the anti-ferromagnetic condensate ground state at extremely low magnetic fields.
Sahoo, Shaon; Durga Prasad Goli, V M L; Sen, Diptiman; Ramasesha, S
2014-07-01
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(F)(1)) and antiferromagnetic (J(A)(1)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(F)(2)). In this model frustration is present due to the non-zero J(F)(2). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(F)(2)and large J(F)(1)/J(A)(1). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(F)(1), the phase diagram in the space of J(A)(1)-J(F)(2) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian. PMID:24935169
Spin wave dynamics in Heisenberg ferromagnetic/antiferromagnetic single-walled nanotubes
NASA Astrophysics Data System (ADS)
Mi, Bin-Zhou
2016-09-01
The spin wave dynamics, including the magnetization, spin wave dispersion relation, and energy level splitting, of Heisenberg ferromagnetic/antiferromagnetic single-walled nanotubes are systematically calculated by use of the double-time Green's function method within the random phase approximation. The role of temperature, diameter of the tube, and wave vector on spin wave energy spectrum and energy level splitting are carefully analyzed. There are two categories of spin wave modes, which are quantized and degenerate, and the total number of independent magnon branches is dependent on diameter of the tube, caused by the physical symmetry of nanotubes. Moreover, the number of flat spin wave modes increases with diameter of the tube rising. The spin wave energy and the energy level splitting decrease with temperature rising, and become zero as temperature reaches the critical point. At any temperature, the energy level splitting varies with wave vector, and for a larger wave vector it is smaller. When pb=π, the boundary of first Brillouin zone, spin wave energies are degenerate, and the energy level splittings are zero.
The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains
Fertitta, Edoardo; Paulus, Beate; El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry
2015-12-28
The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection S{sub z} has been derived.
Contrasting distributions of pairwise entanglement and mutual information in Heisenberg spin systems
NASA Astrophysics Data System (ADS)
Subrahmanyam, V.
2016-08-01
The correlations between a pair of spins in a many-spin state encoded in the diagonal and off-diagonal spin-spin correlation functions. These spin functions determine the quantum correlation measures, like pair-wise concurrence, quantum discord and other measures of quantum information. We show that for isotropic and translationally invariant states, the quantum correlations depend only on the diagonal spin correlation function. The pair concurrence shows a strict short-ranged behavior. The distribution of concurrence for a random W-like state exhibits a long tail for both time-reversal invariant states and for states that break the time reversal. The quantum discord can be related to the diagonal spin correlation function. As the spin function is long range close to a critical point, analogously the quantum discord exhibits a long range behavior. For the isotropic state, the conditional entropy distribution is a Dirac delta function, whereas it has a twin-peak structure for the anisotropic model.
Kosevich, Yuriy A; Gann, Vladimir V
2013-06-19
We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.
Spin liquid nature in the Heisenberg J1-J2 triangular antiferromagnet
NASA Astrophysics Data System (ADS)
Iqbal, Yasir; Hu, Wen-Jun; Thomale, Ronny; Poilblanc, Didier; Becca, Federico
2016-04-01
We investigate the spin-1/2 Heisenberg model on the triangular lattice in the presence of nearest-neighbor J1 and next-nearest-neighbor J2 antiferromagnetic couplings. Motivated by recent findings from density-matrix renormalization group (DMRG) claiming the existence of a gapped spin liquid with signatures of spontaneously broken lattice point group symmetry [Zhu and White, Phys. Rev. B 92, 041105 (2015), 10.1103/PhysRevB.92.041105 and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403 (2015), 10.1103/PhysRevB.92.140403], we employ the variational Monte Carlo (VMC) approach to analyze the model from an alternative perspective that considers both magnetically ordered and paramagnetic trial states. We find a quantum paramagnet in the regime 0.08 ≲J2/J1≲0.16 , framed by 120∘ coplanar (stripe collinear) antiferromagnetic order for smaller (larger) J2/J1 . By considering the optimization of spin-liquid wave functions of a different gauge group and lattice point group content as derived from Abrikosov mean-field theory, we obtain the gapless U(1 ) Dirac spin liquid as the energetically most preferable state in comparison to all symmetric or nematic gapped Z2 spin liquids so far advocated by DMRG. Moreover, by the application of few Lanczos iterations, we find the energy to be the same as the DMRG result within error bars. To further resolve the intriguing disagreement between VMC and DMRG, we complement our methodological approach by the pseudofermion functional renormalization group (PFFRG) to compare the spin structure factors for the paramagnetic regime calculated by VMC, DMRG, and PFFRG. This model promises to be an ideal test bed for future numerical refinements in tracking the long-range correlations in frustrated magnets.
NASA Astrophysics Data System (ADS)
Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki
2016-09-01
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.
Majumdar, Kingshuk
2011-03-23
The effects of interlayer coupling and spatial anisotropy on the spin-wave excitation spectra of a three-dimensional spatially anisotropic, frustrated spin-½ Heisenberg antiferromagnet (HAFM) are investigated for the two ordered phases using second-order spin-wave expansion. We show that the second-order corrections to the spin-wave energies are significant and find that the energy spectra of the three-dimensional HAFM have similar qualitative features to the energy spectra of the two-dimensional HAFM on a square lattice. We also discuss the features that can provide experimental measures for the strength of the interlayer coupling, spatial anisotropy parameter, and magnetic frustration.
NASA Astrophysics Data System (ADS)
Hu, Wen-Jun; Zhu, Wei; Zhang, Yi; Gong, Shoushu; Becca, Federico; Sheng, D. N.
2015-01-01
We investigate the extended Heisenberg model on the kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor superexchanges are considered, we find that a gapped spin liquid described by nontrivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with a C =1 /2 fractionalized Chern number.
NASA Astrophysics Data System (ADS)
Wills, A. S.; Zhitomirsky, M. E.; Canals, B.; Sanchez, J. P.; Bonville, P.; Dalmas de Réotier, P.; Yaouanc, A.
2006-01-01
Low-temperature powder neutron diffraction measurements are performed in the ordered magnetic state of the pyrochlore antiferromagnet Gd2Sn2O7. Symmetry analysis of the diffraction data indicates that this compound has the ground state predicted theoretically for a Heisenberg pyrochlore antiferromagnet with dipolar interactions. The difference in the magnetic structure of Gd2Sn2O7 andof nominally analogous Gd2Ti2O7 is found to be determined by a specific type of third-neighbour superexchange interaction on the pyrochlore lattice between spins across empty hexagons.
NASA Astrophysics Data System (ADS)
Guo, J. L.; Song, H. S.
2010-01-01
We study the thermal entanglement in the two-qubit Heisenberg XXZ model with the Dzyaloshinskii-Moriya (DM) interaction, and teleport an unknown state using the model in thermal equilibrium state as a quantum channel. The effects of DM interaction, including Dx and Dz interaction, the anisotropy and temperature on the entanglement and fully entangled fraction are considered. What deserves mentioning here is that for the antiferromagnetic case, the Dx interaction can be more helpful for increasing the entanglement and critical temperature than Dz, but this cannot for teleportation.
NASA Astrophysics Data System (ADS)
Barnes, T.
In this article we review numerical studies of the quantum Heisenberg antiferromagnet on a square lattice, which is a model of the magnetic properties of the undoped “precursor insulators” of the high temperature superconductors. We begin with a brief pedagogical introduction and then discuss zero and nonzero temperature properties and compare the numerical results to analytical calculations and to experiment where appropriate. We also review the various algorithms used to obtain these results, and discuss algorithm developments and improvements in computer technology which would be most useful for future numerical work in this area. Finally we list several outstanding problems which may merit further investigation.
Strečka, Jozef; Ekiz, Cesur
2015-05-01
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice. PMID:26066155
Flux 1/fα noise in two-dimensional Heisenberg spin glasses: Effects of weak anisotropic interactions
NASA Astrophysics Data System (ADS)
Atalaya, Juan; Clarke, John; Schön, Gerd; Shnirman, Alexander
2014-07-01
We study the dynamics of a two-dimensional ensemble of randomly distributed classical Heisenberg spins with isotropic RKKY and weaker anisotropic dipole-dipole couplings. Such ensembles may give rise to the flux noise observed in SQUIDs with a 1/fα power spectrum with α ≲1. We solve numerically the Landau-Lifshitz-Gilbert equations of motion in the dissipationless limit. We find that Ising-type fluctuators, which arise from spin clustering close to a spin-glass critical behavior with Tc=0, give rise to 1/fα noise. Even weak anisotropic interactions lead to a crossover from the Heisenberg-type criticality to the much stronger Ising-type criticality. The temperature-dependent exponent α (T)≲1 increases and approaches unity when the temperature is lowered. This mechanism acts in parallel to the spin diffusion mechanism. Whereas the latter is sensitive to the device geometry, the spin-clustering mechanism is largely geometry independent.
Tanamoto, Tetsufumi; Ono, Keiji; Liu, Yu-xi; Nori, Franco
2015-01-01
Hamiltonian engineering is an important approach for quantum information processing, when appropriate materials do not exist in nature or are unstable. So far there is no stable material for the Kitaev spin Hamiltonian with anisotropic interactions on a honeycomb lattice, which plays a crucial role in the realization of both Abelian and non-Abelian anyons. Here, we show two methods to dynamically realize the Kitaev spin Hamiltonian from the conventional Heisenberg spin Hamiltonian using pulse-control techniques based on the Baker-Campbell-Hausdorff (BCH) formula. In the first method, the Heisenberg interaction is changed into Ising interactions in the first process of the pulse sequence. In the next process of the first method, we transform them to a desirable anisotropic Kitaev spin Hamiltonian. In the second more efficient method, we show that if we carefully design two-dimensional pulses that vary depending on the qubit location, we can obtain the desired Hamiltonian in only one step of applying the BCH formula. As an example, we apply our methods to spin qubits based on quantum dots, in which the effects of both the spin-orbit interaction and the hyperfine interaction are estimated. PMID:26081899
Mehra, J.
1987-05-01
In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schroedinger during 1920-1927 are treated. From the formulation of quantum mechanics in 1925-1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory - formulated in fall 1926 by Dirac, London, and Jordan - Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publicly enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of quantum mechanics and of physical theory as such - formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930 - were continued during the next decades. All these aspects are briefly summarized.
NASA Astrophysics Data System (ADS)
Tahir-Kheli, R. A.
1984-02-01
An exact expression for the small-dilution correction to the long-wavelength spin-wave dispersion in Heisenberg ferromagnets at low temperatures is derived by the transcription of the analysis of the preceding paper. Numerical results to six decimal places are presented for a variety of exchange integrals extending up to the third-neighbor shell.
NASA Astrophysics Data System (ADS)
Strečka, Jozef; Alécio, Raphael Cavalcante; Lyra, Marcelo L.; Rojas, Onofre
2016-07-01
The spin-1/2 Ising-Heisenberg three-leg tube composed of the Heisenberg spin triangles mutually coupled through the Ising inter-triangle interaction is exactly solved in a zero magnetic field. By making use of the local conservation for the total spin on each Heisenberg spin triangle the model can be rigorously mapped onto a classical composite spin-chain model, which is subsequently exactly treated through the transfer-matrix method. The ground-state phase diagram, correlation functions, concurrence, Bell function, entropy and specific heat are examined in detail. It is shown that the spin frustration represents an indispensable ground for a thermal entanglement, which is quantified by the quantum concurrence. The specific heat displays diverse temperature dependences, which may include a sharp low-temperature peak mimicking a temperature-driven first-order phase transition. It is convincingly evidenced that this anomalous peak originates from massive thermal excitations from the doubly degenerate ground state towards an excited state with a high macroscopic degeneracy due to chiral degrees of freedom of the Heisenberg spin triangles.
NASA Astrophysics Data System (ADS)
Kleemans, Machiel
2010-11-01
The book Heisenberg and the Interpretation of Quantum Mechanics—The Physicist as Philosopher, by Kristian Camilleri is critically reviewed. The work details Heisenberg’s philosophical development from an early positivist commitment towards a later philosophy of language. It is of interest to researchers and graduate students in the history and philosophy of quantum mechanics.
ERIC Educational Resources Information Center
Hadzidaki, Pandora
2008-01-01
In this paper, we present a multi-dimensional study concerning Heisenberg's "gamma ray microscope", a thought experiment, which is intimately connected with the historical development of quantum mechanics (QM), and also with the most disputed interpretations of quantum theory. In this study: (a) we investigate how philosophers of science read and…
ERIC Educational Resources Information Center
Velentzas, Athanasios; Halkia, Krystallia
2011-01-01
In this work an attempt is made to explore the possible value of using Thought Experiments (TEs) in teaching physics to upper secondary education students. Specifically, a qualitative research project is designed to investigate the extent to which the Thought Experiment (TE) called "Heisenberg's Microscope", as it has been transformed by Gamow for…
NASA Astrophysics Data System (ADS)
Rapini, M.; Dias, R. A.; Costa, B. V.
2007-01-01
Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase (I), a phase characterized by a change from out-of-plane to in-plane in the magnetization (II), and a high-temperature paramagnetic phase (III). It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phases II and III is of the BKT type.
NASA Astrophysics Data System (ADS)
Liu, Yu; Hu, Ai-Yuan; Wang, Huai-Yu
2016-08-01
We study a two-dimensional Heisenberg ferrimagnet composed of spin-1 and spin-3/2 sublattices considering both exchange and single-ion anisotropies. The adjoint effects of the two anisotropies on the possible compensation point are investigated. It is concluded that a primary condition for the compensation point to appear is that the single-ion anisotropy of the smaller spins should be nonzero and be greater than a certain value which depends on other parameters. The exchange anisotropy can raise the compensation point slightly. The thermodynamic functions are evaluated. All the thermodynamic functions with various parameter values are smooth no matter whether there is a compensation point or not. Thus, from the thermodynamic functions, one is unable to judge if the compensation occurs.
Majumdar, Kingshuk
2011-02-01
The magnetic phase diagram of a spatially anisotropic, frustrated spin-[Formula: see text] Heisenberg antiferromagnet on a stacked square lattice is investigated using a second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Néel and stripe) separated by a paramagnetic disordered phase. Within the second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.
NASA Astrophysics Data System (ADS)
Li, Peng; Su, Haibin; Dong, Hui-Ning; Shen, Shun-Qing
2009-08-01
We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interactions J1 and third-nearest-neighbor interactions J3 by means of Schwinger-boson mean-field theory. By setting an antiferromagnetic J3 and varying J1 from positive to negative values, we disclose the low-temperature features of its interesting incommensurate phase. The gapless dispersion of quasiparticles leads to the intrinsic T2 law of specific heat. The magnetic susceptibility is linear in temperature. The local magnetization is significantly reduced by quantum fluctuations. We address possible relevance of these results to the low-temperature properties of NiGa2S4. From a careful analysis of the incommensurate spin wavevector, the interaction parameters are estimated as J1≈-3.8755 K and J3≈14.0628 K, in order to account for the experimental data.
NASA Astrophysics Data System (ADS)
Huang, Li-Yuan; Fang, Mao-Fa
2008-07-01
The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of the noisy quantum channel are studied in detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.
NASA Astrophysics Data System (ADS)
Iqbal, Yasir; Becca, Federico; Poilblanc, Didier
2011-03-01
The highly frustrated spin-(1)/(2) quantum Heisenberg model with both nearest (J1) and next-nearest (J2) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBCs) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a small ferromagnetic next-nearest-neighbor exchange coupling |J2|>0.09J1 leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL; instead it possesses a nontrivial flux pattern and large dimerization.
Hovhannisyan, V V; Strečka, J; Ananikian, N S
2016-03-01
The spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins is rigorously solved using the transfer-matrix method. In particular, exact results for the ground state, magnetization process and specific heat are presented and discussed. It is shown that further-neighbor interaction between nodal spins gives rise to three novel ground states with a translationally broken symmetry, but at the same time, does not increases the total number of intermediate plateaus in a zero-temperature magnetization curve compared with the simplified model without this interaction term. The zero-field specific heat displays interesting thermal dependencies with a single- or double-peak structure. PMID:26836749
NASA Astrophysics Data System (ADS)
Kamppeter, T.; Mertens, F. G.; Sánchez, Angel; Gronbech-Jensen, N.; Bishop, A. R.; Dominguez-Adame, F.
The 2-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry bears non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. In order to study the dynamics of these vortices under thermal fluctuations we use the Landau-Lifshitz equation and add white noise and Gilbert damping. Using a collective variable theory we derive an equation of motion with stochastic forces which are shown to represent white noise with an effective diffusion constant. We compare the results with Langevin dynamics simulations for the Landau-Lifshitz equation and find three temperature regimes: For low temperatures the dynamics is described by a 3rd-order equation of motion, for intermediate temperatures by a 1st-order equation. For higher temperatures, but still below the Kosterlitz-Thouless transition temperature, the spontaneous appearance of vortex-antivortex pairs does not allow a single-particle description.
Field-Induced Quantum Phase Transitions in S = 1/2 J1-J2 Heisenberg Model on Square Lattice
NASA Astrophysics Data System (ADS)
Morita, Katsuhiro; Shibata, Naokazu
2016-09-01
We study the magnetic field dependence of the ground state of the S = 1/2 J1-J2 Heisenberg model on the square lattice by the density matrix renormalization group (DMRG) method. With the use of the sine-square deformation, we obtain eight different ground states including plaquette valence-bond crystal with a finite spin gap, transverse Néel, transverse stripe, 1/2 magnetization plateau with up-up-up-down (uuud), and three new states we named the Y-like, V-like, and Ψ states around J2/J1 = 0.55-0.6. The phase transitions from the transverse Néel (at J2/J1 = 0.55) and stripe (at J2/J1 = 0.6) states to the uuud and Y-like states, respectively, are discontinuous, as in the case of a spin flop.
NASA Astrophysics Data System (ADS)
Hovhannisyan, V. V.; Strečka, J.; Ananikian, N. S.
2016-03-01
The spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins is rigorously solved using the transfer-matrix method. In particular, exact results for the ground state, magnetization process and specific heat are presented and discussed. It is shown that further-neighbor interaction between nodal spins gives rise to three novel ground states with a translationally broken symmetry, but at the same time, does not increases the total number of intermediate plateaus in a zero-temperature magnetization curve compared with the simplified model without this interaction term. The zero-field specific heat displays interesting thermal dependencies with a single- or double-peak structure.
NASA Astrophysics Data System (ADS)
Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiao-Gang
2016-08-01
The ground state phase of a spin-1/2 J1-J2 antiferromagnetic Heisenberg model on a square lattice around the maximally frustrated regime (J2˜0.5 J1 ) has been debated for decades. Here we study this model using the cluster update algorithm for tensor-product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with exact diagonalization study. Through finite size scaling of the spin correlation function, we find the critical point J2c1=0.572 (5 ) J1 and critical exponents ν =0.50 (8 ) ,ηs=0.28 (6 ) . In the range of 0.572
NASA Astrophysics Data System (ADS)
Morita, Katsuhiro; Shibata, Naokazu
2016-10-01
We study the ground state of the S =1/2 Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at M /Msat=0 ,1/4 ,3/8 ,1/2 , and 3/4 , where Msat is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a 4 √{2 }×2 √{2 } magnetic unit cell with a 16-fold degeneracy.
Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3.
Singh, Yogesh; Manni, S; Reuther, J; Berlijn, T; Thomale, R; Ku, W; Trebst, S; Gegenwart, P
2012-03-23
Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2IrO3 (A=Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ≈-125 K for Na2IrO3 to θ≈-33 K for Li2IrO3, while the ordering temperature remains roughly the same T(N)≈15 K. Using functional renormalization group calculations we show that this evolution of θ and T(N) as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2IrO3 is deep in a magnetically ordered regime, while Li2IrO3 appears to be close to a spin-liquid regime.
Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates A2IrO3
Singh Y.; Berlijn T.; Singh, Y.; Manni, S.; Reuther, J.; Thomale, R.; Ku, W.; Trebst, S.; Gegenwart, P.
2012-03-23
Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A{sub 2}IrO{sub 3} (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S = 1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from {Theta} {approx} -125 K for Na{sub 2}IrO{sub 3} to {Theta} {approx} -33 K for Li{sub 2}IrO{sub 3}, while the ordering temperature remains roughly the same T{sub N} {approx} 15 K. Using functional renormalization group calculations we show that this evolution of {Theta} and T{sub N} as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na{sub 2}IrO{sub 3} is deep in a magnetically ordered regime, while Li{sub 2}IrO{sub 3} appears to be close to a spin-liquid regime.
NASA Astrophysics Data System (ADS)
Ito, Kazuhiro; Shimahara, Hiroshi
2016-02-01
We examine the mean field theory of a uniaxial coupled Heisenberg antiferromagnet with two subsystems, one of which consists of strongly interacting small spins and the other consists of weakly interacting large spins. We reanalyze the experimental data of specific heat and magnetic susceptibility obtained by previous authors for the organic compound λ-(BETS)2FeCl4 at low temperatures, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. The model parameters for this compound are evaluated, where the applicability of the theory is checked. As a result, it is found that J1 ≫ J12 ≫ J2, where J1, J2, and J12 denote the exchange coupling constant between π spins, that between 3d spins, and that between π and 3d spins, respectively. At the low-temperature limit, both sublattice magnetizations of the 3d and π spins are saturated, and the present model is reduced to the Schottky model, which successfully explains experimental observations in previous studies. As temperature increases, fluctuations of 3d spins increase, while π spins remain almost saturated. Near the critical temperature, both spins fluctuate significantly, and thus the mean field approximation breaks down. It is revealed that the magnetic anisotropy, which may be crucial to the antiferromagnetic long-range order, originates from J12 rather than from J2 and that the angle between the magnetic easy-axis and the crystal c-axis is approximately 26-27° in the present effective model.
DMRG Study of the S >= 1 quantum Heisenberg Antiferromagnet on a Kagome-like lattice without loops
NASA Astrophysics Data System (ADS)
Lamberty, R. Zach; Changlani, Hitesh J.; Henley, Christopher L.
2013-03-01
The Kagome quantum Heisenberg antiferromagnet, for spin up to S = 1 and perhaps S = 3 / 2 , is a prime candidate to realize a quantum spin liquid or valence bond crystal state, but theoretical or computational studies for S > 1 / 2 are difficult and few. We consider instead the same interactions and S >= 1 on the Husimi Cactus, a graph of corner sharing triangles whose centers are vertices of a Bethe lattice, using a DMRG procedure tailored for tree graphs. Since both lattices are locally identical, properties of the Kagome antiferromagnet dominated by nearest-neighbor spin correlations should also be exhibited on the Cactus, whereas loop-dependent effects will be absent on the loopless Cactus. Our study focuses on the possible transition(s) that must occur with increasing S for the Cactus antiferromagnet. (It has a disordered valence bond state at S = 1 / 2 but a 3-sublattice coplanar ordered state in the large S limit). We also investigate the phase diagram of the S = 1 quantum XXZ model with on-site anisotropy, which we expect to have three-sublattice and valence-bond-crystal phases similar to the kagome case. This work is supported by the National Science Foundation through a Graduate Research Fellowship to R. Zach Lamberty, as well as grant DMR-
NASA Astrophysics Data System (ADS)
Liu, Guang-Hua; Dou, Jun-Ya; Lu, Peng
2016-03-01
The effect of the Dzyaloshinskii-Moriya interaction (DMI) on ground-state phase diagrams of spin-1 Heisenberg-Ising alternating chains is investigated by the infinite time-evolving block decimation method. Three rich phase diagrams for three cases with different DMIs are obtained and discussed systematically. The DMI on even bonds plays a key role in the ground-state phase diagram, especially the appearance of the Haldane phase. However, the DMI on odd bonds seems to have very weak effect on the phase diagram. Both the odd- and even-string orders become nonzero in the Haldane phase, and have their maximum values at θ = π. For the odd-dimer phase, the even-string correlator vanishes absolutely despite varying θ, but a double-peak structure of the odd-string correlator is observed. Odd-string correlator becomes maximum at θ = π / 2 and 3 π / 2, but vanishes at θ = π. It indicates that the generalized string correlator can be used to distinguish the odd-dimer from the Haldane phase. Doubly degenerate entanglement spectrum is observed in the Haldane phase, which can be regarded as a clear signature of the existence of topological orders. Strong enough transverse nearest-neighbor correlations are found to be very important for the appearance of the Haldane and the odd-dimer phases.
NASA Astrophysics Data System (ADS)
Zhuo, W. Z.; Qin, M. H.; Dong, S.; Li, X. G.; Liu, J.-M.
2016-03-01
In this paper, we study a biquadratic Heisenberg model with coupled orbital degrees of freedom by using a Monte Carlo simulation to investigate the phase transitions in iron-based superconductors. The antiferroquadrupolar state, which may be related to the magnetism of FeSe [R. Yu and Q. Si, Phys. Rev. Lett. 115, 116401 (2015), 10.1103/PhysRevLett.115.116401], is stabilized by the anisotropic biquadratic interaction induced by a ferro-orbital-ordered state. It is revealed that the orbital and nematic transitions occur at the same temperature for all the cases, supporting the mechanism of the orbital-driven nematicity as revealed in most recent experiments [S. H. Baek, D. V. Efremov, J. M. Ok, J. S. Kim, J. van den Brink, and B. Büchner, Nat. Mater. 14, 210 (2015), 10.1038/nmat4138]. In addition, it is suggested that the orbital interaction may lead to the separation of the structural and magnetic phase transitions, as observed in many families of iron pnictides.
Néel to spin-Peierls transition in a quasi-one-dimensional Heisenberg model coupled to bond phonons
NASA Astrophysics Data System (ADS)
Pillay, Jason Cornelius; Wierschem, Keola; Sengupta, Pinaki
2013-08-01
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-(1)/(2) Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless Néel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the Néel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc shows a second order phase transition. The variation of the equilibrium bond length distortion δeq with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
Ground-state phases of the spin-1 J1-J2 Heisenberg antiferromagnet on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Li, P. H. Y.; Bishop, R. F.
2016-06-01
We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling J1>0 and frustrating next-nearest-neighbor coupling J2≡κ J1>0 , using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range 0 <κ <1 we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice Néel order for κ <κc1=0.250(5 ) , and another with four-sublattice Néel-II order for κ >κc 2=0.340 (5 ) . Two different paramagnetic phases are found to exist in the intermediate region. Over the range κc1<κ<κci=0.305 (5 ) we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range κci<κ <κc 2 we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.
NASA Astrophysics Data System (ADS)
Müller, Patrick; Richter, Johannes; Hauser, Andreas; Ihle, Dieter
2015-06-01
We use the spin-rotation-invariant Green's function method as well as the high-temperature expansion to discuss the thermodynamic properties of the frustrated spin-SJ1-J2 Heisenberg magnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighbor bonds J1< 0 and antiferromagnetic next-nearest-neighbor bonds J2 ≥ 0 and arbitrary spin S. We find that the transition point J_2^c between the ferromagnetic ground state and the antiferromagnetic one is nearly independent of the spin S, i.e., it is very close to the classical transition point J_2c,clas = 2/3|J_1|. At finite temperatures we focus on the parameter regime J_2
NASA Astrophysics Data System (ADS)
Mazurova, Elena; Lapshin, Aleksey
2013-04-01
The method of discrete linear transformations that can be implemented through the algorithms of the Standard Fourier Transform (SFT), Short-Time Fourier Transform (STFT) or Wavelet transform (WT) is effective for calculating the components of the deflection of the vertical from discrete values of gravity anomaly. The SFT due to the action of Heisenberg's uncertainty principle indicates weak spatial localization that manifests in the following: firstly, it is necessary to know the initial digital signal on the complete number line (in case of one-dimensional transform) or in the whole two-dimensional space (if a two-dimensional transform is performed) in order to find the SFT. Secondly, the localization and values of the "peaks" of the initial function cannot be derived from its Fourier transform as the coefficients of the Fourier transform are formed by taking into account all the values of the initial function. Thus, the SFT gives the global information on all frequencies available in the digital signal throughout the whole time period. To overcome this peculiarity it is necessary to localize the signal in time and apply the Fourier transform only to a small portion of the signal; the STFT that differs from the SFT only by the presence of an additional factor (window) is used for this purpose. A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa. The STFT makes it possible to improve spatial localization, that is, it allows one to define the presence of any frequency in the signal and the interval of its presence. However, owing to Heisenberg's uncertainty principle, it is impossible to tell
NASA Astrophysics Data System (ADS)
Shimahara, Hiroshi; Ito, Kazuhiro
2014-11-01
We examine a two-dimensional (2D) coupled antiferromagnetic (AF) Heisenberg model that consists of two subsystems: an isotropic S = 1/2 spin subsystem with strong AF exchange interactions (main system), and a uniaxial S = 5/2 spin subsystem with weak exchange interactions. This model is an example in which additional semiclassical degrees of freedom affect a quantum system; it also describes a possible stabilization mechanism of AF long-range order (LRO) in the 2D organic compound λ-(BETS)2FeCl4, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. Previous experimental studies have revealed that 3d spins on FeCl4 anions passively follow the AF LRO of the π-electron system in the BETS layers, although the AF LRO is stabilized by the 3d spins themselves. To explain this paradoxical behavior, we examine a scenario in which the uniaxial anisotropy of the 3d spins stabilizes the AF LRO on an isotropic 2D π-spin system. We extend Green's function theory, called the Tyablikov approximation, to the present system, which describes spin-wave excitations and is consistent with the Mermin-Wagner theorem. It is shown that even extremely weak interactions with the uniaxial subsystem efficiently stabilize the AF LRO in the main system, even in the absence of AF exchange interactions in the uniaxial subsystem. The AF LRO is triggered by the uniaxial subsystem, but the sublattice magnetization remains smaller than that of the main system in the high-temperature region. These results are consistent with experimental data for λ-(BETS)2FeCl4 and λ-(BETS)2GaCl4; the latter does not have the 3d spins and does not exhibit the AF LRO.
Murtazaev, A. K.; Ramazanov, M. K. Badiev, V. K.
2012-08-15
The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J{sub 1}) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = vertical bar J{sub 1}/J vertical bar = 0-0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.
Phase diagram of the spin-1/2 triangular J1-J2 Heisenberg model on a three-leg cylinder
NASA Astrophysics Data System (ADS)
Saadatmand, S. N.; Powell, B. J.; McCulloch, I. P.
2015-06-01
We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest- and next-nearest-neighbor spin-exchange coupling, on three-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range 120∘ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are nonchiral and planar. We also identify the nature of phase transitions.
NASA Astrophysics Data System (ADS)
Schwandt, David; Mambrini, Matthieu; Poilblanc, Didier
2010-06-01
We propose a general nonperturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective generalized quantum dimer models. We develop the formal lattice-independent frame and establish some important results on (i) the locality of the generated Hamiltonians, (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian—shown to capture the essential properties and provide deep insights on the microscopic model [D. Poilblanc, M. Mambrini, and D. Schwandt, Phys. Rev. B 81, 180402(R) (2010)]—is derived.
Schwandt, David; Mambrini, Matthieu; Poilblanc, Didier
2010-06-01
We propose a general nonperturbative scheme that quantitatively maps the low-energy sector of spin-1/2 frustrated Heisenberg antiferromagnets to effective generalized quantum dimer models. We develop the formal lattice-independent frame and establish some important results on (i) the locality of the generated Hamiltonians, (ii) how full resummations can be performed in this renormalization scheme. The method is then applied to the much debated kagome antiferromagnet for which a fully resummed effective Hamiltonian - shown to capture the essential properties and provide deep insights on the microscopic model [D. Poilblanc, M. Mambrini, and D. Schwandt, Phys. Rev. B 81, 180402(R) (2010)] - is derived.
NASA Astrophysics Data System (ADS)
Moujaes, Elie A.; Khater, A.; Abou Ghantous, M.
2015-10-01
Ferromagnetic phase diagrams were, for a long time, unsuccessfully determined theoretically, despite the important Callen's 1963 [21] theoretical model. A great variety of experimental data for the magnetization over the entire range of temperature defining the ordered phase compared well with an empirical formula recently determined by Kuz'min (2005) [22]. Nonetheless, the Ising effective field theory (EFT), which can be of enormous support to both methods, was never given attention. The present work intends to show how the Ising EFT technique, when combined with the Green functions in Callen's work, is able to reconcile theoretical work with experimental data. The ratio kTc / JZS(S + 1) plays an important role in finding values for the exchange parameter J, whose first-principles calculation, often depending on the package used, is not properly done. J can be determined for a variety of ferromagnetic materials represented by general spin systems S with a number of nearest neighbours Z and critical temperature Tc, even for models including a percolative feature, characteristic of diluted interactive systems. We demonstrate that EFT is capable of estimating a value of J, which can substitute the use of more complex theoretical models or the performance of ab initio/DFT calculations.
Dynamic properties of magnets with spin S = 3/2 and non-Heisenberg isotropic interaction
Kosmachev, O. A.; Fridman, Yu. A.; Galkina, E. G.; Ivanov, B. A.
2015-02-15
The dynamic properties of a magnet with magnetic-ion spin of 3/2 and an isotropic spin interaction of a general form have been investigated. Only four phase states can be realized in the system under consideration at various relationships between the material parameters: the ferro- and antiferromagnetic phases with saturated spin and the states with tensor order parameters, the nematic and antinematic ones. For these phases, the spontaneous symmetry breaking is determined by the octupole order parameter containing the mean values trilinear in spin operator components at a given site. The spectra of elementary excitations have been determined in all phases. Additional branches of excitations arise in all four phase states.
Dynamical Properties of a Diluted Dipolar-Interaction Heisenberg Spin Glass
NASA Astrophysics Data System (ADS)
Zhang, Kai-Cheng; Liu, Yong; Chi, Feng
2014-02-01
Up to now the chirality is seldom studied in the diluted spin glass although many investigations have been performed on the site-ordered Edwards—Anderson model. By simulation, we investigate the dynamical properties of both the spin-glass and the chiral-glass phases in a diluted dipolar system, which was manifested to have a spin-glass transition by recent numerical study. By scaling we find that both phases have the same aging behavior and closer aging parameter μ. Similarly, the domains grow in the same way and both phases have a closer barrier exponent Ψ. It means that both the spins and the chirality have the same dynamical properties and they may freeze at the same temperature.
NASA Astrophysics Data System (ADS)
Zobov, V. E.; Kucherov, M. M.
2016-06-01
Singular points of the autocorrelation function on the imaginary time axis that is averaged over the location of spins in the magnetically dilute spin lattice with isotropic spin-spin interaction at a high temperature have been studied. For the autocorrelation function in the approximation of the self-consistent fluctuating local field, nonlinear integral equations have been proposed which reflect the separation of the inhomogeneous spin systems into close spins and other spins. The coordinates of the nearest singular points have been determined in terms of the radius of convergence of the expansion in powers of time, the coefficients of which have been calculated from recurrence equations. It has been shown that the coordinates of singular points and, consequently, the wings of the autocorrelation function spectrum at strong magnetic dilution are determined by the modulation of the local field by the nearest pairs of spins leading to its logarithmic concentration dependence.
Superconductivity. Fermi arcs in a doped pseudospin-1/2 Heisenberg antiferromagnet.
Kim, Y K; Krupin, O; Denlinger, J D; Bostwick, A; Rotenberg, E; Zhao, Q; Mitchell, J F; Allen, J W; Kim, B J
2014-07-11
High-temperature superconductivity in cuprates arises from an electronic state that remains poorly understood. We report the observation of a related electronic state in a noncuprate material, strontium iridate (Sr2IrO4), in which the distinct cuprate fermiology is largely reproduced. Upon surface electron doping through in situ deposition of alkali-metal atoms, angle-resolved photoemission spectra of Sr2IrO4 display disconnected segments of zero-energy states, known as Fermi arcs, and a gap as large as 80 millielectron volts. Its evolution toward a normal metal phase with a closed Fermi surface as a function of doping and temperature parallels that in the cuprates. Our result suggests that Sr2IrO4 is a useful model system for comparison to the cuprates. PMID:24925913
Chirality and Z2 vortices in a Heisenberg spin model on the kagome lattice
NASA Astrophysics Data System (ADS)
Domenge, J.-C.; Lhuillier, C.; Messio, L.; Pierre, L.; Viot, P.
2008-05-01
The phase diagram of the classical J1-J2 model on the kagome lattice is investigated by using extensive Monte Carlo simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of the chiral order is preempted by the first-order proliferation of Z2 point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both Z2 defects and gapless magnons contribute to disordering the system at very low temperatures. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.
Construction of coherent states for physical algebraic systems
Hassouni, Y.; Curado, E.M.F.; Rego-Monteiro, M.A.
2005-02-01
We construct a general state which is an eigenvector of the annihilation operator of the generalized Heisenberg algebra. We show, for several systems characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.
Verification of generic fidelity recovery in a dynamical system
NASA Astrophysics Data System (ADS)
Pineda, Carlos; Schäfer, Rudi; Prosen, Tomaž; Seligman, Thomas
2006-06-01
We study the time evolution of fidelity in a dynamical many-body system, namely, a kicked Ising model, modified to allow for a time-reversal invariance breaking. We find good agreement with the random matrix predictions in the realm of strong perturbations. In particular for the time-reversal symmetry breaking case the predicted revival at the Heisenberg time is clearly seen.
Exact steady states for quantum quenches in integrable Heisenberg spin chains
NASA Astrophysics Data System (ADS)
Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale
2016-08-01
The study of quantum quenches in integrable systems has significantly advanced with the introduction of the quench action method, a versatile analytical approach to nonequilibrium dynamics. However, its application is limited to those cases where the overlaps between the initial state and the eigenstates of the Hamiltonian governing the time evolution are known exactly. Conversely, in this work we consider physically interesting initial states for which such overlaps are still unknown. In particular, we focus on different classes of product states in spin-1 /2 and spin-1 integrable chains, such as tilted ferromagnets and antiferromagnets. We get around the missing overlaps by following a recent approach based on the knowledge of complete sets of quasilocal charges. This allows us to provide a closed-form analytical characterization of the effective stationary state reached at long times after the quench, through the Bethe ansatz distributions of particles and holes. We compute the asymptotic value of local correlations and check our predictions against numerical data.
Observation of Fermi Arcs in a Doped Pseudospin-1/2 Heisenberg Antiferromagnet Strontium Iridate
NASA Astrophysics Data System (ADS)
Kim, Y. K.; Krupin, O.; Denlinger, J. D.; Bostwick, A.; Rotenberg, E.; Zhao, Q.; Mitchell, J. F.; Allen, J. W.; Kim, B. J.
2015-03-01
Emergent properties of two microscopically different systems can be similar. Despite manifestly different underlying microscopic electronic structures, the effective low-energy physics of Sr2IrO4 has been shown to be remarkably similar to that of the parent insulators of superconducting cuprates. However, whether the parallel with the cuprates continues to hold for a metallic phase induced by carrier doping remains unclear, which holds the key to the realization of a new high temperature superconductor. In this presentation, we will report that the evolution of the fermiology of Sr2IrO4 with doping and temperature reproduces that observed for the cuprates. Upon surface electron doping through in situ deposition of alkali-metal atoms, angle-resolved photoemission spectra of Sr2IrO4 display disconnected segments of zero-energy states, known as `Fermi arcs', and a gap as large as 80 meV. The Fermi arc smoothly evolves to a closed Fermi surface at higher surface coverage and at higher temperature.
Singular eigenstates in the even(odd) length Heisenberg spin chain
NASA Astrophysics Data System (ADS)
Ranjan Giri, Pulak; Deguchi, Tetsuo
2015-05-01
We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \\{{{λ }α }\\} are invariant under the sign changes of their rapidities \\{{{λ }α }\\}=\\{-{{λ }α }\\}, then the Bethe ansatz equations are reduced to a system of (M-2)/2((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N=3(2k+1) with k=1,2,3,\\cdots . It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.
NASA Astrophysics Data System (ADS)
Ghosh, Pratyay; Verma, Akhilesh Kumar; Kumar, Brijesh
2016-01-01
A spin-1 Heisenberg model on trimerized kagome lattice is studied by doing a low-energy bosonic theory in terms of plaquette triplons defined on its triangular unit cells. The model considered has an intratriangle antiferromagnetic exchange interaction J (set to 1) and two intertriangle couplings J'>0 (nearest neighbor) and J″ (next nearest neighbor; of both signs). The triplon analysis performed on this model investigates the stability of the trimerized singlet ground state (which is exact in the absence of intertriangle couplings) in the J'-J″ plane. It gives a quantum phase diagram that has two gapless antiferromagnetically ordered phases separated by the spin-gapped trimerized singlet phase. The trimerized singlet ground state is found to be stable on J″=0 line (the nearest-neighbor case), and on both sides of it for J″≠0 , in an extended region bounded by the critical lines of transition to the gapless antiferromagnetic phases. The gapless phase in the negative J″ region has a coplanar 120∘ antiferromagnetic order with √{3 }×√{3 } structure. In this phase, all the magnetic moments are of equal length, and the angle between any two of them on a triangle is exactly 120∘. The magnetic lattice in this case has a unit cell consisting of three triangles. The other gapless phase, in the positive J″ region, is found to exhibit a different coplanar antiferromagnetic order with ordering wave vector q =(0 ,0 ) . Here, two magnetic moments in a triangle are of the same magnitude, but shorter than the third. While the angle between two short moments is 120∘-2 δ , it is 120∘+δ between a short and the long one. Only when J″=J' , their magnitudes become equal and the relative angles 120∘. The magnetic lattice in this q =(0 ,0 ) phase has the translational symmetry of the kagome lattice with triangular unit cells of reduced (isosceles) symmetry. This reduction in the point-group symmetry is found to show up as a difference in the intensities of
NASA Astrophysics Data System (ADS)
Jiang, F. J.
2012-12-01
The low-energy constants, namely the staggered magnetization density M˜ s per spin, the spin stiffness ρ s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M˜ s and ρ s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M˜ s , ρ s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M˜ s = 0.26882(3), ρ s = 0.1012(2) J, and c = 1.2905(8) Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.
NASA Astrophysics Data System (ADS)
Mehra, Jagdish
1987-05-01
In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger during 1920 1927 are treated. From the formulation of quantum mechanics in 1925 1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory—formulated in fall 1926 by Dirac, London, and Jordan—Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publicly enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of qnautum mechanics and of physical theory as such—formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930—were continued during the next decades. All these aspects are briefly summarized.
NASA Astrophysics Data System (ADS)
Yannouleas, Constantine; Brandt, Benedikt B.; Landman, Uzi
2016-07-01
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t–J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.
NASA Astrophysics Data System (ADS)
Yannouleas, Constantine; Brandt, Benedikt B.; Landman, Uzi
2016-07-01
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.
Accardi, Luigi; Boukas, Andreas
2010-06-17
In previous papers we have shown that the one mode Heisenberg algebra Heis(1) admits a unique non-trivial central extensions CeHeis(1) which can be realized as a sub-Lie-algebra of the Schroedinger algebra, in fact the Galilei Lie algebra. This gives a natural family of unitary representations of CeHeis(1) and allows an explicit determination of the associated group by exponentiation. In contrast with Heis(1), the group law for CeHeis(1) is given by nonlinear (quadratic) functions of the coordinates. The vacuum characteristic and moment generating functions of the classical random variables canonically associated to CeHeis(1) are computed. The second quantization of CeHeis(1) is also considered.
NASA Astrophysics Data System (ADS)
Xiao, Y.; Kumar, C. M. N.; Nandi, S.; Su, Y.; Jin, W. T.; Fu, Z.; Faulhaber, E.; Schneidewind, A.; Brückel, Th.
2016-06-01
High-resolution inelastic neutron scattering reveals that the elementary magnetic excitations in multiferroic MnWO4 consist of low-energy dispersive electromagnons in addition to the well-known spin-wave excitations. The latter can well be modeled by a Heisenberg Hamiltonian with magnetic exchange coupling extending to the 12th nearest neighbor. They exhibit a spin-wave gap of 0.61(1) meV. Two electromagnon branches appear at lower energies of 0.07(1) and 0.45(1) meV at the zone center. They reflect the dynamic magnetoelectric coupling and persist in both the collinear magnetic and paraelectric AF1 phase and the spin spiral ferroelectric AF2 phase. These excitations are associated with the Dzyaloshinskii-Moriya exchange interaction, which is significant due to the rather large spin-orbit coupling.
NASA Astrophysics Data System (ADS)
Becca, Federico; Iqbal, Yasir; Poilblanc, Didier
2011-03-01
The highly-frustrated spin- 1 / 2 quantum Heisenberg model with both nearest (J1) and next-nearest (J2) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBC) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a small ferromagnetic next-nearest-neighbor exchange coupling |J2 | > 0.09J1 leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL: instead it possesses a non-trivial flux pattern and large dimerization.
NASA Astrophysics Data System (ADS)
Mutka, H.; Payen, C.; Molinié, P.; Soubeyroux, J. L.; Colombet, P.; Taylor, A. D.
1991-07-01
The spin correlations of the S=1 Heisenberg antiferromagnetic chains in AgVP2S6 have been studied by neutron scattering at temperatures of the order of T~10-2 J/kB. On the polycrystalline samples, with a careful choice of experimental conditions, we have observed a Haldane gap of Eg=26 meV at the antiferromagnetic point at q=π. The excitation spectra are consistent with a mode that has a spin-wave velocity C=150 meV and a correlation length ξ~=5.5, close to C/Eg. These results are in quantitative agreement with the predictions and numerical results on the Haldane state.
Huang, Yi-Zhen; Xi, Bin; Chen, Xi; Li, Wei; Wang, Zheng-Chuan; Su, Gang
2016-06-01
The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J>0 in the armchair direction and ferromagnetic interaction J^{'}<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q_{2} and spin stiffness ρ in two directions for various coupling ratios α=J^{'}/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point α_{c}=-0.93. Through the finite-size scaling analysis on Q_{2}, ρ_{x}, and ρ_{y}, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α. A phase diagram in the coupling ratio α-magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C(T) for different α's intersects precisely at one point, similar to that of liquid ^{3}He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q_{2}, ρ, and C(T) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds. PMID:27415211
NASA Astrophysics Data System (ADS)
Huang, Yi-Zhen; Xi, Bin; Chen, Xi; Li, Wei; Wang, Zheng-Chuan; Su, Gang
2016-06-01
The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J >0 in the armchair direction and ferromagnetic interaction J'<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q2 and spin stiffness ρ in two directions for various coupling ratios α =J'/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point αc=-0.93 . Through the finite-size scaling analysis on Q2, ρx, and ρy, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α . A phase diagram in the coupling ratio α -magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C (T ) for different α 's intersects precisely at one point, similar to that of liquid 3He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q2, ρ , and C (T ) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.
NASA Astrophysics Data System (ADS)
Del Maestro, Adrian; Gingras, Michel J. P.
2007-08-01
The Gd2Sn2O7 pyrochlore Heisenberg antiferromagnet displays a phase transition to a four sublattice Néel ordered state at a critical temperature Tc˜1K . The low-temperature state found via neutron scattering corresponds to that predicted by a classical model that considers nearest-neighbor antiferromagnetic exchange and long-range dipolar interactions. Despite the seemingly conventional nature of the ordered state, the specific heat Cv has been found to be described in the temperature range 350mK⩽T⩽800mK by an anomalous power law Cv˜T2 . A similar temperature dependence of Cv has also been reported for Gd2Ti2O7 , another pyrochlore Heisenberg material. Such behavior is to be contrasted with the typical T3 behavior expected for a three-dimensional antiferromagnet with conventional long-range order which is then generally accompanied by an exp(-Δ/T) behavior at lower temperature where anisotropy effects induce a gap Δ to collective spin excitations. Such anomalous T2 behavior in Cv has been argued to be correlated to an unusual energy dependence of the density of states which also seemingly manifests itself in low-temperature spin fluctuations found in muon spin relaxation experiments. In this paper, we report calculations of Cv that consider spin-wave-like excitations out of the Néel order observed in Gd2Sn2O7 via neutron scattering. We argue that the parametric Cv∝T2 does not reflect the true low-energy excitations of Gd2Sn2O7 . Rather, we find that the low-energy excitations of this material are antiferromagnetic magnons gapped by single-ion and dipolar anisotropy effects, and that the lowest temperature of 350mK considered in previous specific heat measurements accidentally happens to coincide with a crossover temperature below which magnons become thermally activated and Cv takes an exponential form. We argue that further specific heat measurements that extend down to at least 100mK are required in order to ascribe an unconventional description of
Krajniak, Wiktor
2014-01-01
The purpose of this article is the analyses of discussion between Albert Einstein and Werner Heisenberg in the period 1925-1927. Their disputes, relating to the sources of scientific knowledge, its methods and the value of knowledge acquired in this way, are part of the characteristic for the European science discourse between rationalism and empirism. On the basis of some sources and literature on the subject, the epistemological positions of both scholars in the period were reconstructed. This episode, yet poorly known, is a unique example of scientific disputes, whose range covers a broad spectrum of methodological problems associated with the historical development of science. The conducted analysis sheds some light on the source of popularity of logical empirism in the first half of the 20th century. A particular emphasis is placed on the impact of the neopositivist ideas which reflect Heisenberg's research program, being the starting point for the Copenhagen interpretation of quantum mechanics. The main assumption of logical empirism, concerning acquisition of scientific knowledge only by means of empirical procedures and logical analysis of the language of science, in view of the voiced by Einstein arguments, bears little relationship with actual testing practices in the historical aspect of the development of science. The criticism of Heisenberg's program, carried out by Einstein, provided arguments for the main critics of the neopositivist ideal and contributed to the bankruptcy of the idea of logical empirism, thereby starting a period of critical rationalism prosperity, arising from criticism of neopositivism and alluding to Einstein's ideas.
Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang
2015-04-29
Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e. the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e. an antiferromagnetic (AF), AF stripe, odd- and even-Haldane phases, is obtained. These phases are found to be separated by continuous QPTs: the topological QPT between the odd- and even-Haldane phases is verified to be continuous and corresponds to conformal field theory with central charge c = 1; while the rest of the phase transitions in the phase diagram are found to be c = 1/2. We also revisit, with our MPS method, the exactly solvable case of HIAC model with DM interactions only on odd bonds and find that the even-Haldane phase disappears, but the other three phases, i.e. the AF, AF stripe and odd-Haldane phases, still remain in the phase diagram. We exhibit the evolution of the even-Haldane phase by tuning the DM interactions on the even bonds gradually. PMID:25817273
Cattes, Stefanie M; Gubbins, Keith E; Schoen, Martin
2016-05-21
In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases. PMID:27208962
NASA Astrophysics Data System (ADS)
Carvalho, D. C.; Pires, A. S. T.; Mól, L. A. S.
2016-06-01
We examine the phase diagram of the spin-1 J1 -J2 -J3 ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice, in which J1 is the ferromagnetic exchange interaction between nearest neighbors, J2 is the antiferromagnetic exchange interaction between next-nearest neighbors and J3 is the antiferromagnetic exchange interaction between next-next-nearest neighbors. Using the bond-operator formalism, we investigate the phase transitions between the disordered paramagnetic phase and the ordered ones. We show that the nature of the quantum phase transitions changes as the frustration parameters (J2/J1, J3/J1) are varied. The zero-temperature phase diagram exhibits second- and first-order transitions, depending on the energy gap behavior. Remarkably, we find a disordered nonmagnetic phase, even in the absence of a crystal field, which is suggested to be a quantum spin liquid candidate. We also depict the phase diagram at finite temperature for some values of crystal field and frustration parameters.
NASA Astrophysics Data System (ADS)
Kumar, Krishna; Changlani, Hitesh J.; Clark, Bryan K.; Fradkin, Eduardo
2016-10-01
We perform an exact-diagonalization study of the spin-1/2 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization m =2/3 with an emphasis on the X Y point (Jz=0 ) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014), 10.1103/PhysRevB.90.174409] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of σx y=1/2 . Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the σx y=1/2 CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.
Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang
2015-04-29
Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e. the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e. an antiferromagnetic (AF), AF stripe, odd- and even-Haldane phases, is obtained. These phases are found to be separated by continuous QPTs: the topological QPT between the odd- and even-Haldane phases is verified to be continuous and corresponds to conformal field theory with central charge c = 1; while the rest of the phase transitions in the phase diagram are found to be c = 1/2. We also revisit, with our MPS method, the exactly solvable case of HIAC model with DM interactions only on odd bonds and find that the even-Haldane phase disappears, but the other three phases, i.e. the AF, AF stripe and odd-Haldane phases, still remain in the phase diagram. We exhibit the evolution of the even-Haldane phase by tuning the DM interactions on the even bonds gradually.
Cattes, Stefanie M; Gubbins, Keith E; Schoen, Martin
2016-05-21
In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.
NASA Astrophysics Data System (ADS)
Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin
2016-05-01
In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.
NASA Astrophysics Data System (ADS)
Mi, Bin-Zhou
2016-07-01
The thermodynamic properties of the frustrated arbitrary spin-S J1-J2 Heisenberg antiferromagnet on the body-centered-cubic lattice for Néel phase are systematically calculated by use of the double-time Green's function method within the random phase approximation (RPA). The role of spin quantum number and frustration strength on sublattice magnetization, Néel temperature, internal energy, and free energy are carefully analyzed. The curve of zero-temperature sublattice magnetization
NASA Astrophysics Data System (ADS)
Ramazanoglu, Mehmet; Sapkota, A.; Pandey, A.; Johnston, D.; Goldman, Alan; Kreyssig, A.; Abernathy, D.; Niedziela, J.; Stone, M.; McQueeney, R. J.
Low temperature powder inelastic neutron scattering measurements (INS) were performed on powders of Ba(1-x)KxMn2As2 with x=0(BMA),0.125 and 0.25. BMA is a G type antiferromagnet (AFM) which has local magnetic modulations bridging between the pnictide and cuprate superconductors. Hole doping (K) introduces more metallic behavior. The magnetic contribution to the intensities were retrieved by subtracting the estimated phonon background obtained at high momentum transfers from the raw. The resultant estimated magnetic intensities were analyzed by using damped harmonic oscillator model. The K doping effects create a broadening in the magnetic peak profiles consistent with expected weak FM fluctuations. We also analyzed the INS data using a powder integration routine which is based on J1-J2-Jz Heisenberg Model. The Monte Carlo integration technique is used to obtain the powder-averaged S(Q,E) for a series of Js. The representative values (with lowest chi-squared) obtained for BMA are in agreement with previous results. The values obtained for K doped samples were found in the close proximity to the parent ones. Overall we conclude that the original AFM structure seen in BMA retained its character even in the K doped samples with minimal differences. Work at Ames Laboratory is supported by USDOE under Contract No. DE-AC02-07CH11358 and Work at ITU is supported by TUBITAK 2232.
Identifying Local and Quasilocal Conserved Quantities in Integrable Systems
NASA Astrophysics Data System (ADS)
Mierzejewski, Marcin; Prelovšek, Peter; Prosen, Tomaž
2015-04-01
We outline a procedure for counting and identifying a complete set of local and quasilocal conserved operators in integrable lattice systems. The method yields a systematic generation of all independent, conserved quasilocal operators related to the time average of local operators with a support on up to M consecutive sites. As an example, we study the anisotropic Heisenberg spin-1 /2 chain and show that the number of independent conserved operators grows linearly with M . In addition to the known local operators, there exist novel quasilocal conserved quantities in all the parity sectors. The existence of quasilocal conserved operators is shown also for the isotropic Heisenberg model. Implications for the anomalous relaxation of quenched systems are discussed as well.
Exact quantum dynamics of spin systems using the positive-P representation
NASA Astrophysics Data System (ADS)
Ng, Ray; Sorensen, Erik
2011-03-01
We discuss a scheme for simulating the exact real time quantum dynamics of interacting quantum spin systems within the positive-P formalism. As model systems we study the transverse field Ising model as well as the Heisenberg model undergoing a quench away from the classical ferromagnetic ordered state. In using the positive-P representation (PPR), the dynamics of the interacting quantum spin system is mapped onto a set of stochastic differential equations (SDEs). The number of which scales linearly with the number of spins, N, compared to an exact solution through diagonalization that in the case of the Heisenberg model would require matrices exponentially large in N. This mapping is exact and can in principle be extended to higher dimensional interacting systems as well as to systems with an explicit coupling to the environment. We compare the results from using a PPR approach based on both the optical coherent states as well as SU(2) Radcliff coherent states.
NASA Astrophysics Data System (ADS)
Shimokawa, Tokuro; Watanabe, Ken; Kawamura, Hikaru
2015-10-01
Inspired by the recent theoretical suggestion that the random-bond S =1 /2 antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this "random-singlet state" might be relevant to the QSL behaviors experimentally observed in triangular organic salts κ -(ET) 2Cu2(CN) 3 and EtMe3Sb [Pd(dmit)2] 2 and in kagome herbertsmithite ZnCu3(OH) 6Cl2 , we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, S (q ) and S (q ,ω ) , by means of an exact diagonalization method. In both triangular and kagome models, the computed S (q ,ω ) in the random-singlet state depends on the wave vector q only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy ω . Especially in the strongly random kagome model, S (q ,ω ) hardly depends on q , and exhibits an almost flat distribution for a wide range of ω , together with a ω =0 peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.
Lifting mean field degeneracies in anisotropic spin systems
NASA Astrophysics Data System (ADS)
Sizyuk, Yuriy; Perkins, Natalia; Wolfle, Peter
We propose a method for calculating the fluctuation contribution to the free energy of anisotropic spin systems with generic bilinear superexchange magnetic Hamiltonian based on the Hubbard-Stratonovich transformation. We show that this contribution splits the set of mean field degenerate states with rotational symmetry, and chooses states with the order parameter directed along lattice symmetric directions as the true ground states. We consider the simple example of Heisenberg-compass model on cubic lattice to show that depending on the relative strength of the compass and Heisenberg interactions the spontaneous magnetization is pinned to either one of the cubic directions or one of the cubic body diagonals with a intermediate phase in between where the minima and maxima of the free energy interchange. DMR-1005932, DMR-1511768, and NSF PHY11-25915.
NASA Astrophysics Data System (ADS)
Temme, F. P.
1991-06-01
For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the Sn-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl-kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the Sn partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel'fand pattern algebra of SU(2) and SU(2)×Sn tensor bases over Liouville space is presented together with both the related s-boson algebras and a description of the associated {||2k 0>>} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×Sn induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.
Some properties of correlations of quantum lattice systems in thermal equilibrium
Fröhlich, Jürg; Ueltschi, Daniel
2015-05-15
Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.
Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System.
Žnidarič, Marko; Scardicchio, Antonello; Varma, Vipin Kerala
2016-07-22
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects, we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems. PMID:27494464
Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System
NASA Astrophysics Data System (ADS)
Žnidarič, Marko; Scardicchio, Antonello; Varma, Vipin Kerala
2016-07-01
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects, we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.
NASA Astrophysics Data System (ADS)
Schilling, R.; Schütz, H.; Ghadimi, A. H.; Sudhir, V.; Wilson, D. J.; Kippenberg, T. J.
2016-05-01
Placing a nanomechanical object in the evanescent near field of a high-Q optical microcavity gives access to strong gradient forces and quantum-limited displacement readout, offering an attractive platform for both precision sensing technology and basic quantum optics research. Robustly implementing this platform is challenging, however, as it requires integrating optically smooth surfaces separated by ≲λ /10 . Here we describe an exceptionally high-cooperativity, single-chip optonanomechanical transducer based on a high-stress Si3N4 nanobeam monolithically integrated into the evanescent near field of SiO2 microdisk cavity. Employing a vertical integration technique based on planarized sacrificial layers, we realize beam-disk gaps as little as 25 nm while maintaining mechanical Q f >1012 Hz and intrinsic optical Q ˜107. The combination of low loss, small gap, and parallel-plane geometry results in radio-frequency flexural modes with vacuum optomechanical coupling rates of 100 kHz, single-photon cooperativities in excess of unity, and large zero-point frequency (displacement) noise amplitudes of 10 kHz (fm )/√ Hz . In conjunction with the high power-handling capacity of SiO2 and low extraneous substrate noise, the transducer performs particularly well as a sensor, with recent deployment in a 4-K cryostat realizing a displacement imprecision 40 dB below that at the standard quantum limit (SQL) and an imprecision-backaction product <5 ℏ [Wilson et al., Nature (London) 524, 325 (2015)]. In this report, we provide a comprehensive description of device design, fabrication, and characterization, with an emphasis on extending Heisenberg-limited readout to room temperature. Towards this end, we describe a room-temperature experiment in which a displacement imprecision 32 dB below that at the SQL and an imprecision-backaction product <60 ℏ is achieved. Our results extend the outlook for measurement-based quantum control of nanomechanical oscillators and suggest an
Generalized Heisenberg theory of turbulence
NASA Technical Reports Server (NTRS)
Uberoi, M. S.; Narain, J. P.
1974-01-01
Solutions of the generalized theory are obtained which are consistent with the previous work on energy transfer measurements. They also agree with the measurements of turbulent energy spectrum for wave numbers in the universal equilibrium range.
Heisenberg groups and noncommutative fluxes
Freed, Daniel S. . E-mail: dafr@math.utexas.edu; Moore, Gregory W.; Segal, Graeme
2007-01-15
We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an uncertainty relation which obstructs simultaneous measurement of electric and magnetic flux when torsion fluxes are included. Next, we show how to define the Hilbert space of a self-dual field. The Hilbert space is Z{sub 2}-graded and we show that, in general, self-dual theories (including the RR fields of string theory) have fermionic sectors. We indicate how rational conformal field theories associated to the two-dimensional Gaussian model generalize to (4k+2)-dimensional conformal field theories. When our ideas are applied to the RR fields of string theory we learn that it is impossible to measure the K-theory class of a RR field. Only the reduction modulo torsion can be measured.
NASA Astrophysics Data System (ADS)
Paduan-Filho, A.; Oliveira, N. F.; Bindilatti, V.; Foner, S.; Shapira, Y.
2003-12-01
A theory for the equilibrium low-temperature magnetization M of a diluted Heisenberg antiferromagnetic chain is presented. Only the nearest-neighbor (NN) exchange interaction is included, and the distribution of the magnetic ions is assumed to be random. Values of the magnetic fields Bi at the magnetization steps (MST’s) from finite chains with two to five spins (pairs, triplets, quartets, and quintets) are given for chains composed of spins S=5/2. The magnitudes of these MST’s as a function of the fraction, x, of cations that are magnetic are given for any S. An expression for the apparent saturation value of M is derived. The magnetization curve, M versus B, is calculated using the exact contributions of finite chains with one to five spins, and the “rise and ramp approximation” for longer chains. An expression for the low-temperature saturation magnetic field Bs(n) of a finite chain with n spins is given. Some nonequilibrium effects that occur in a rapidly changing B are also considered. Some of these result from the absence of thermal equilibrium within the sample itself, whereas others are caused by the absence of thermal equilibrium between the sample and its environment (e.g., liquid-helium bath). Specific nonequilibrium models based on earlier treatments of the phonon bottleneck, and of spin flips associated with cross relaxation and with level crossings (anticrossings), are discussed. Magnetization data on powders of TMMC diluted with cadmium [i.e., (CH3)4NMnxCd1-xCl3, with 0.16⩽x⩽0.50] were measured at 0.55 K in 18-T superconducting magnets. The field B1 at the first MST from pairs is used to determine the NN exchange constant J. This J/kB changes from -5.9 K to -6.5 K as x increases from 0.16 to 0.50. The magnetization curves obtained in the superconducting magnets are compared with simulations based on the equilibrium theory. A reasonably good agreement is found. Data for the differential susceptibility, dM/dB, were taken in pulsed magnetic
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
Aydogmus, F.
2015-02-15
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.
NASA Astrophysics Data System (ADS)
Popkov, Vladislav; Salerno, Mario
2013-06-01
In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.
NASA Astrophysics Data System (ADS)
Popkov, Vladislav; Salerno, Mario
2012-11-01
In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.
Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
NASA Astrophysics Data System (ADS)
Chaloupka, Jiří; Khaliullin, Giniyat
2016-08-01
We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster ground states using a particular set of spin-coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron-diffraction and resonant x-ray-diffraction data on Na2IrO3 and RuCl3 and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.
Measures of quantum synchronization in continuous variable systems.
Mari, A; Farace, A; Didier, N; Giovannetti, V; Fazio, R
2013-09-01
We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems. PMID:25166668
Cope, F W
1981-01-01
The Weber psychophysical law, which describes much experimental data on perception by man, is derived from the Heisenberg uncertainty principle on the assumption that human perception occurs by energy detection by superconductive microregions within man . This suggests that psychophysical perception by man might be considered merely a special case of physical measurement in general. The reverse derivation-i.e., derivation of the Heisenberg principle from the Weber law-may be of even greater interest. It suggest that physical measurements could be regarded as relative to the perceptions by the detectors within man. Thus one may develop a "human" theory of relativity that could have the advantage of eliminating hidden assumptions by forcing physical theories to conform more completely to the measurements made by man rather than to concepts that might not accurately describe nature.
Order From disorder in Frustrated Spin Systems
NASA Astrophysics Data System (ADS)
Coleman, Piers
This talk will review the phemomenon of ''Order from disorder'': the mechanism by which fluctuations remove a degeneracy within a frustrated spin system. An important consequence of order-from-disorder, is the ability of frustrated Heisenberg spin systems to overcome the Mermin-Wagner theorem, developing new forms of discrete order, even when the spins themselves remain disordered with a finite correlation length. The most well-known example, is the two-dimensional frustrated J1 -J2 Heisenberg model, which undergoes a finite temperature Ising phase transition into a stripy or ''nematic'' state, even though the spins do not order until absolute zero. Nematic ordering of this kind is believed to occur in the iron-based superconductors, such as BaFe2 As2 . More recently, it has been possible to theoretically study the triangular-honeycomb versions of the J1 -J2 model, called a windmill model, in which order-from disorder drives the development of six-state clock order. Remarkably, in this case, order-from-disorder leads to an intermediate power-law spin phase, despite the underlying Heisenerg spins. This research was supported by DOE Basic Energy Sciences Grant DE-FG02-99ER45790.
Self-Induced Glassiness and Pattern Formation in Spin Systems Subject to Long-Range Interactions
NASA Astrophysics Data System (ADS)
Principi, Alessandro; Katsnelson, Mikhail I.
2016-09-01
We study the glass formation in two- and three-dimensional Ising and Heisenberg spin systems subject to competing interactions and uniaxial anisotropy with a mean-field approach. In three dimensions, for sufficiently strong anisotropy the systems always modulate in a striped phase. Below a critical strength of the anisotropy, a glassy phase exists in a finite range of temperature, and it becomes more stable as the system becomes more isotropic. In two dimensions the criticality is always avoided and the glassy phase always exists.
Miller, William H; Cotton, Stephen J
2016-08-28
It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements. PMID:27586896
Ghorbani, Elaheh; Shahbazi, Farhad; Mosadeq, Hamid
2016-10-12
Using the modified spin wave method, we study the [Formula: see text] Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For a symmetric S = 1/2 model, with the same couplings for all the equivalent neighbors, we find three phases in terms of the frustration parameter [Formula: see text]: (1) a commensurate collinear ordering with staggered magnetization (Néel.I state) for [Formula: see text], (2) a magnetically gapped disordered state for [Formula: see text], preserving all the symmetries of the Hamiltonian and lattice, which by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of the three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Néel.II state), for [Formula: see text]. We also explore the phase diagram of a distorted [Formula: see text] model with S = 1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal phase in addition to the previous three phases found for the undistorted model. PMID:27518832
Miller, William H; Cotton, Stephen J
2016-08-28
It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.
Ghorbani, Elaheh; Shahbazi, Farhad; Mosadeq, Hamid
2016-10-12
Using the modified spin wave method, we study the [Formula: see text] Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For a symmetric S = 1/2 model, with the same couplings for all the equivalent neighbors, we find three phases in terms of the frustration parameter [Formula: see text]: (1) a commensurate collinear ordering with staggered magnetization (Néel.I state) for [Formula: see text], (2) a magnetically gapped disordered state for [Formula: see text], preserving all the symmetries of the Hamiltonian and lattice, which by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of the three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Néel.II state), for [Formula: see text]. We also explore the phase diagram of a distorted [Formula: see text] model with S = 1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal phase in addition to the previous three phases found for the undistorted model.
Honda, Z.; Katsumata, K.
2001-06-01
We have performed magnetization (M) measurements on the S=1 quasi-one-dimensional Heisenberg antiferromagnet, Ni(C{sub 5}H{sub 14}N{sub 2}){sub 2}N{sub 3}(PF{sub 6}) (NDMAP) with a vibrating sample magnetometer in a static field (H). In the temperature (T) dependence of the susceptibility (M/H), we observed that a transition from the gapped phase to a gapless one occurs at a finite H. On increasing H further, we observed a bending in the M/H{endash}T curve and the M/H takes almost constant value below the bending temperature (T{sub B}). Since T{sub B} corresponds to the critical temperature determined from heat capacity measurements, we identify the T independent susceptibility to the perpendicular susceptibility of an anisotropic antiferromagnet. We also observed a change in the M{endash}H curves of NDMAP at finite H. The value of H where M changes corresponds to the phase boundary between the field induced long-range ordered and paramagnetic phases determined from the heat capacity measurement. {copyright} 2001 American Institute of Physics.
NASA Astrophysics Data System (ADS)
Ghorbani, Elaheh; Shahbazi, Farhad; Mosadeq, Hamid
2016-10-01
Using the modified spin wave method, we study the {{J}1}-{{J}2} Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For a symmetric S = 1/2 model, with the same couplings for all the equivalent neighbors, we find three phases in terms of the frustration parameter \\barα={{J}2}/{{J}1} : (1) a commensurate collinear ordering with staggered magnetization (Néel.I state) for 0≤slant \\barα≲ 0.207 , (2) a magnetically gapped disordered state for 0.207≲ \\barα≲ 0.369 , preserving all the symmetries of the Hamiltonian and lattice, which by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of the three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Néel.II state), for 0.396≲ \\barα≤slant 1 . We also explore the phase diagram of a distorted {{J}1}-{{J}2} model with S = 1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal phase in addition to the previous three phases found for the undistorted model.
NASA Astrophysics Data System (ADS)
Miller, William H.; Cotton, Stephen J.
2016-08-01
It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.
Soft Modes, Localization, and Two-Level Systems in Spin Glasses.
Baity-Jesi, M; Martín-Mayor, V; Parisi, G; Perez-Gaviro, S
2015-12-31
In the three-dimensional Heisenberg spin glass in a random field, we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For a not too large field the density of states g(ω) develops localized soft plastic modes and reaches zero as ω(4) (for large fields a gap appears). When we perturb the system adding a force along the softest mode, one reaches very similar minima of the energy, separated by small barriers, that appear to be good candidates for classical two-level systems. PMID:26765021
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
2014-08-01
We consider the minimal bosonization realization of supersymmetric shape-invariant systems where generalized supercharge operators are constructed using the partner supersymmetric operators, the parameter potential translation formalism and the reflection operator. We obtain the solution of the eigenvalue equation and study the quantum dynamics of the supersymmetric system including terms in the Hamiltonian which are constructed using the combination of the bosonized supercharge operators. The connections between the bosonized supersymmetric formalism, the Bose-Fermi transformation and the generalization of the R-deformed Heisenberg algebra are discussed. As an illustration, we apply the generalized formalism for the case of the trigonometric Rosen-Morse potential.
Schmidtke, Daniel; Gemmer, Jochen
2016-01-01
Closed quantum systems obey the Schrödinger equation, whereas nonequilibrium behavior of many systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type spin models comprising 12-20 spins. The accuracy to which these conditions are met increases with system size.
Schmidtke, Daniel; Gemmer, Jochen
2016-01-01
Closed quantum systems obey the Schrödinger equation, whereas nonequilibrium behavior of many systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type spin models comprising 12-20 spins. The accuracy to which these conditions are met increases with system size. PMID:26871042
Distribution of Quantum Coherence in Multipartite Systems.
Radhakrishnan, Chandrashekar; Parthasarathy, Manikandan; Jambulingam, Segar; Byrnes, Tim
2016-04-15
The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or is distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence. PMID:27127948
Reduced Operator Approximation for Modelling Open Quantum Systems
NASA Astrophysics Data System (ADS)
Werpachowska, A.
2015-06-01
We present the reduced operator approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order in the system-bath interaction operators, defining them for either general quantum harmonic oscillator baths or specialising them for independent baths with Lorentzian spectral densities. Its wide applicability is demonstrated on the examples of systems coupled to different baths (with varying system-bath interaction strength and bath memory length), and compared with the exact pseudomode and the popular quantum state diffusion approach. The method captures the decoherence of the system interacting with the bath, while conserving the total energy. Our results suggest that quantum coherence effects persist in open quantum systems for much longer times than previously thought.
Dillenschneider, Raoul; Richert, Jean
2006-06-01
We study the effect of site occupation in two-dimensional quantum spin systems at finite temperature in a {pi}-flux state description at the mean-field level. We impose each lattice site to be occupied by a single SU(2) spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a QED{sub 3} Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.
Mehlig, B; Müller, K; Eckhardt, B
1999-05-01
We consider distributions of diagonal matrix elements for smooth observables in systems whose classical phase space has a mixture of chaotic and nearly integrable regions. The quantum distributions agree very well with distributions obtained from classical trajectory segments whose length is the Heisenberg time. Non-Gaussian wings in the distributions can be linked to classical trapping in certain parts of phase space, sometimes connected to islands, but also to regions separated by other barriers to transport. Thus classical deviations from ergodicity are quantitatively reflected in quantum matrix elements. The relation to scars is discussed.
The free energy in a class of quantum spin systems and interchange processes
NASA Astrophysics Data System (ADS)
Björnberg, J. E.
2016-07-01
We study a class of quantum spin systems in the mean-field setting of the complete graph. For spin S = 1/2, the model is the Heisenberg ferromagnet, and for general spin S ∈ 1/2 N, it has a probabilistic representation as a cycle-weighted interchange process. We determine the free energy and the critical temperature (recovering results by Tóth and by Penrose when S = 1/2). The critical temperature is shown to coincide (as a function of S) with that of the q = 2S + 1 state classical Potts model, and the phase transition is discontinuous when S ≥ 1.
Magnetic properties of Ni(C 5H 5N) 2Ni(CN) 4 - 2d S = 1 Heisenberg magnet with easy-axis anisotropy
NASA Astrophysics Data System (ADS)
Čižmár, E.; Kačmár, M.; Orendáč, M.; Orendáčová, A.; Černák, J.; Feher, A.
1999-05-01
Specific heat studies of structurally layered powdered Ni(C 5H 5N) 2Ni(CN) 4 have been carried out from 100 mK to 2.5 K in zero magnetic field. A λ-like anomaly with a strong rounding-off observed at 0.9 K might be ascribed to the phase transition into the magnetically ordered state. Consequently, easy-axis type of anisotropy introduced by C 5H 5N enabled analysing the system using a 2d S = {1}/{2} Ising model for the square lattice and a Schottky anomaly yielding D/ kB = - 1.9 K and | J/ kB| = 0.35 K.
NASA Astrophysics Data System (ADS)
Sakaguchi, Takehiro; Kakurai, Kazuhisa; Yokoo, Tetsuya; Akimitsu, Jun
1996-09-01
Magnetic excitations of the ideal one-dimensional, spin S=1, antiferromagnet Y2BaNiO5 are studied by means of inelastic neutron scattering on single crystal sample. Our experimental results at low temperature indicate that Y2BaNiO5 can be regarded as the best isotropic Haldane-system sofar studied with the intrachain exchange energy J/k B=-24.1 meV and the averaged gap Δ(T=7 K)=8.5 meV. Y2BaNiO5 exhibits a good magnetic one-dimensionality with the inter-/intrachain exchange ratio of |J‧/J|≤10-4 and has only very small easy-axis and in-plane single ion anisotropy of |D/J|=0.03 and |E/J|˜0.01. In addition the temperature dependence of the Haldane gap Δ(T) and its damping rate was determined.
Peric, Mirna; Bales, Barney L; Peric, Miroslav
2012-03-22
The work in part 6 of this series (J. Phys. Chem. A 2009, 113, 4930), addressing the task of separating the effects of Heisenberg spin exchange (HSE) and dipole-dipole interactions (DD) on electron paramagnetic resonance (EPR) spectra of nitroxide spin probes in solution, is extended experimentally and theoretically. Comprehensive measurements of perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (pDT) in squalane, a viscous alkane, paying special attention to lower temperatures and lower concentrations, were carried out in an attempt to focus on DD, the lesser understood of the two interactions. Theoretically, the analysis has been extended to include the recent comprehensive treatment by Salikhov (Appl. Magn. Reson. 2010, 38, 237). In dilute solutions, both interactions (1) introduce a dispersion component, (2) broaden the lines, and (3) shift the lines. DD introduces a dispersion component proportional to the concentration and of opposite sign to that of HSE. Equations relating the EPR spectral parameters to the rate constants due to HSE and DD have been derived. By employing nonlinear least-squares fitting of theoretical spectra to a simple analytical function and the proposed equations, the contributions of the two interactions to items 1-3 may be quantified and compared with the same parameters obtained by fitting experimental spectra. This comparison supports the theory in its broad predictions; however, at low temperatures, the DD contribution to the experimental dispersion amplitude does not increase linearly with concentration. We are unable to deduce whether this discrepancy is due to inadequate analysis of the experimental data or an incomplete theory. A new key aspect of the more comprehensive theory is that there is enough information in the experimental spectra to find items 1-3 due to both interactions; however, in principle, appeal must be made to a model of molecular diffusion to separate the two. The permanent diffusion model is used to
Nontrivial ferrimagnetism on the low-dimensional quantum spin systems with frustration
NASA Astrophysics Data System (ADS)
Shimokawa, Tokuro; Nakano, Hiroki; Sakai, Toru
2013-03-01
In low-dimensional quantum spin systems with frustration, nontrivial magnetisms often occur due to strong quantum fluctuation. Ferrimagnetism in non-frustrated systems is well-known to occur from the mechanism based on the Marshall-Lieb-Mattis theorem. This type of ferrimagnetism is called ``Lieb-Mattis (LM) type.'' Recently, the occurrence of nontrivial ferrimagnetism has been reported in some one-dimensional Heisenberg spin systems with frustration, in which the continuous change of spontaneous magnetization and the incommensurate modulation in local magnetization are observed. This type is called ``non-Lieb-Mattis (NLM) type.'' In this study, we tackle a problem whether the NLM ferrimagnetism occurs or not in higher dimensional systems. We investigate the S =1/2 Heisenberg models on the spatially anisotropic two-dimensional (2D) kagome lattice and on the quasi-one-dimensional (Q1D) kagome strip lattices by the numerical diagonalization and density matrix renormalization group methods. The Q1D models share the same structure in their inner part with the spatially anisotropic 2D kagome lattice; we examine two cases with respect to strip width. We will discuss the relationship between the ground-state properties of the Q1D lattices and those of the 2D lattice.
Magnetic correlations in a classic Mott system
Bao, W.; Broholm, C.; Aeppli, G.; Carter, S.A.; Dai, D.; Frost, C.D.; Honig, J.M.; Metcalf, P.
1997-07-01
The metal-insulator transition in V{sub 2}O{sub 3} causes a fundamental change in its magnetism. While the antiferromagnetic insulator (AFI) is a Heisenberg localized spin system, the antiferromagnetism in the strongly correlated metal is determined by a Fermi surface instability. Paramagnetic fluctuations in the metal and insulator represent similar spatial spin correlations, but are unrelated to the long range order in the AFI. The phase transition to the AFI induces an abrupt switching of magnetic correlations to a different magnetic wave vector. The AFI transition, therefore, is not a conventional spin order-disorder transition. Instead it is accounted for by an ordering in the occupation of the two degenerate d-orbitals at the Fermi level.
Quasilocal charges in integrable lattice systems
NASA Astrophysics Data System (ADS)
Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž; Zadnik, Lenart
2016-06-01
We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept concerns the so-called quasilocal conserved quantities, which go beyond the standard perception of locality. Two systematic procedures to rigorously construct families of quasilocal conserved operators based on quantum transfer matrices are outlined, specializing on anisotropic Heisenberg XXZ spin-1/2 chain. Quasilocal conserved operators stem from two distinct classes of representations of the auxiliary space algebra, comprised of unitary (compact) representations, which can be naturally linked to the fusion algebra and quasiparticle content of the model, and non-unitary (non-compact) representations giving rise to charges, manifestly orthogonal to the unitary ones. Various condensed matter applications in which quasilocal conservation laws play an essential role are presented, with special emphasis on their implications for anomalous transport properties (finite Drude weight) and relaxation to non-thermal steady states in the quantum quench scenario.
Entanglement, Nonlinear Dynamics, and the Heisenberg Limit
Pezze, Luca; Smerzi, Augusto
2009-03-13
We show that quantum Fisher information provides a sufficient condition to recognize multiparticle entanglement in an N qubit state. The same criterion gives a necessary and sufficient condition for sub-shot-noise phase sensitivity in the estimation of a collective rotation angle {theta}. The analysis therefore singles out the class of entangled states which are useful to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the nonlinear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.
The Heisenberg representation of quantum computers
Gottesman, D.
1998-06-24
Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.
Nondivergent classical response functions from uncertainty principle: quasiperiodic systems.
Kryvohuz, Maksym; Cao, Jianshu
2005-01-01
Time-divergence in linear and nonlinear classical response functions can be removed by taking a phase-space average within the quantized uncertainty volume O(hn) around the microcanonical energy surface. For a quasiperiodic system, the replacement of the microcanonical distribution density in the classical response function with the quantized uniform distribution density results in agreement of quantum and classical expressions through Heisenberg's correspondence principle: each matrix element (u/alpha(t)/v) corresponds to the (u-v)th Fourier component of alpha(t) evaluated along the classical trajectory with mean action (Ju+Jv)/2. Numerical calculations for one- and two-dimensional systems show good agreement between quantum and classical results. The generalization to the case of N degrees of freedom is made. Thus, phase-space averaging within the quantized uncertainty volume provides a useful way to establish the classical-quantum correspondence for the linear and nonlinear response functions of a quasiperiodic system.
Diffusion and ballistic transport in one-dimensional quantum systems.
Sirker, J; Pereira, R G; Affleck, I
2009-11-20
It has been conjectured that transport in integrable one-dimensional systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling and has not been explained so far. Here, we show that, contrary to common belief, diffusion is universally present in interacting 1D systems subject to a periodic lattice potential. We present a parameter-free formula for the spin-lattice relaxation rate which is in excellent agreement with experiment. Furthermore, we calculate the current decay directly in the thermodynamic limit using a time-dependent density matrix renormalization group algorithm and show that an anomalously large time scale exists even at high temperatures. PMID:20366058
Wu, Feng; Chen, Lingen; Sun, Fengrui; Wu, Chih; Li, Qing
2006-01-01
The purpose of this paper is to establish a model of an irreversible quantum Brayton engine using many noninteracting spin systems as the working substance and consisting of two irreversible adiabatic and two isomagnetic field processes. The time evolution of the total magnetic moment M is determined by solving the generalized quantum master equation of an open system in the Heisenberg picture. The time of two irreversible adiabatic processes is considered based on finite-rate evolution. The relationship between the power output P and the efficiency eta for the irreversible quantum Brayton engine with spin systems is derived. The optimally operating region (or criteria) for the engine is determined. The influences of these important parameters on the performances (P and eta) of the engine are discussed. The results obtained herein will be useful for the further understanding and the selection of the optimal operating conditions for an irreversible quantum Brayton engine with spin systems.
Chung, N. N.; Chew, L. Y.
2007-09-15
We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems.
Theoretical study on perpendicular magnetoelectric coupling in ferroelectromagnet system
NASA Astrophysics Data System (ADS)
Zhong, Chonggui; Jiang, Qing
2002-06-01
We apply the Heisenberg model for antiferromagnetic interaction and Diffour model for ferroelectric interaction to analyze the magnetic, electric, magnetoelectric property in the system with the spontaneous coexistence of the ferroelectric and antiferromagnetic orders below a certain temperature. The soft mode theory is used to calculate the on-site polarization and mean field theory is applied to deal with the on-site magnetization. We also present the perpendicular magnetoelectric susceptibility χme⊥, polarization susceptibility χp as a function of temperature, and discuss the effect of the inherent magnetoelectric coupling on them. In addition, it is found that an anomaly appears in the curve of the polarization susceptibility due to the coupling between the ferroelectric and antiferromagnetic orders.
Classical spin glass system in external field with taking into account relaxation effects
Gevorkyan, A. S. Abajyan, H. G.
2013-08-15
We study statistical properties of disordered spin systems under the influence of an external field with taking into account relaxation effects. For description of system the spatial 1D Heisenberg spin-glass Hamiltonian is used. In addition, we suppose that interactions occur between nearest-neighboring spins and they are random. Exact solutions which define angular configuration of the spin in nodes were obtained from the equations of stationary points of Hamiltonian and the corresponding conditions for the energy local minimum. On the basis of these recurrent solutions an effective parallel algorithm is developed for simulation of stabile spin-chains of an arbitrary length. It is shown that by way of an independent order of N{sup 2} numerical simulations (where N is number of spin in each chain) it is possible to generate ensemble of spin-chains, which is completely ergodic which is equivalent to full self-averaging of spin-chains' vector polarization. Distributions of different parameters (energy, average polarization by coordinates, and spin-spin interaction constant) of unperturbed system are calculated. In particular, analytically is proved and numerically is shown, that for the Heisenberg nearest-neighboring Hamiltonian model, the distribution of spin-spin interaction constants as opposed to widely used Gauss-Edwards-Anderson distribution satisfies Levy alpha-stable distribution law. This distribution is nonanalytic function and does not have variance. In the work we have in detail studied critical properties of an ensemble depending on value of external field parameters (from amplitude and frequency) and have shown that even at weak external fields the spin-glass systemis strongly frustrated. It is shown that frustrations have fractal behavior, they are selfsimilar and do not disappear at scale decreasing of area. By the numerical computation is shown that the average polarization of spin-glass on a different coordinates can have values which can lead to
Propagation of disturbances in degenerate quantum systems
NASA Astrophysics Data System (ADS)
Chancellor, Nicholas; Haas, Stephan
2011-07-01
Disturbances in gapless quantum many-body models are known to travel an unlimited distance throughout the system. Here, we explore this phenomenon in finite clusters with degenerate ground states. The specific model studied here is the one-dimensional J1-J2 Heisenberg Hamiltonian at and close to the Majumdar-Ghosh point. Both open and periodic boundary conditions are considered. Quenches are performed using a local magnetic field. The degenerate Majumdar-Ghosh ground state allows disturbances which carry quantum entanglement to propagate throughout the system and thus dephase the entire system within the degenerate subspace. These disturbances can also carry polarization, but not energy, as all energy is stored locally. The local evolution of the part of the system where energy is stored drives the rest of the system through long-range entanglement. We also examine approximations for the ground state of this Hamiltonian in the strong field limit and study how couplings away from the Majumdar-Ghosh point affect the propagation of disturbances. We find that even in the case of approximate degeneracy, a disturbance can be propagated throughout a finite system.
Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin
2015-03-01
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.
Helical order and multiferroicity in the S =1/2 quasi-kagome system KCu3As2O7(OD)3
NASA Astrophysics Data System (ADS)
Nilsen, G. J.; Okamoto, Y.; Ishikawa, H.; Simonet, V.; Colin, C. V.; Cano, A.; Chapon, L. C.; Hansen, T.; Mutka, H.; Hiroi, Z.
2014-04-01
Several Cu2+ hydroxide minerals have been recently identified as candidate realizations of the S=1/2 kagome Heisenberg model. In this context, we have studied the distorted system KCu3As2O7(OD)3 using neutron scattering and bulk measurements. Although the distortion favors magnetic order over a spin liquid ground state, refinement of the magnetic diffraction pattern below TN1=7.05(5) K yields a complex helical structure with k =(0.77,0,0.11). This structure, as well as the spin excitation spectrum, are well described by a classical Heisenberg model with ferromagnetic nearest neighbor couplings. Multiferroicity is observed below TN1, with an unusual crossover between improper and pseudoproper behavior occurring at TN2=5.5 K. The polarization at T =2 K is P =1.5μCm-2. The properties of KCu3As2O7(OD)3 highlight the variety of physics which arise from the interplay of spin and orbital degrees of freedom in Cu2+ kagome systems.
Enhancement of the magnetic anisotropy barrier in critical long range spin systems.
Borgonovi, F; Celardo, G L
2013-03-13
Magnetic materials are usually characterized by anisotropy energy barriers which dictate the timescale of the magnetization decay and consequently the magnetic stability of the sample. Here we consider magnetization decay for spin systems in a d = 3 cubic lattice with an isotropic Heisenberg interaction decaying as a power law with a critical exponent α = d and on-site anisotropy. We show that the anisotropy energy barrier can be determined from the ergodicity breaking energy of the corresponding isolated system and that, unlike in the case of nearest neighbour interaction, the anisotropy energy barrier grows as the particle volume, V, and not as the cross-sectional area.
Quantum melting of magnetic order in an organic dimer Mott-insulating system
NASA Astrophysics Data System (ADS)
Naka, Makoto; Ishihara, Sumio
2016-05-01
Quantum entanglement effects between the electronic spin and charge degrees of freedom are examined in an organic molecular solid, termed a dimer Mott-insulating system, in which molecular dimers are arranged in a crystal as fundamental units. A low energy effective model includes an antisymmetric exchange interaction, as one of the dominant magnetic interactions. This interaction favors a 90 deg spin configuration, and competes with the Heisenberg-type exchange interaction. Stabilities of the magnetic ordered phases are examined by using the spin-wave theory, as well as the Schwinger-boson theory. It is found that the spin-charge interaction promotes an instability of the long-range magnetic ordered state around a parameter region where two spin-spiral phases are merged. Implication for the quantum spin liquid state observed in κ -(BEDT-TTF)2Cu2 (CN) 3 is discussed.
Modeling complex phenomena: Multiple length and time scales in extended dynamical systems
Lomdahl, P.; Bishop, A.; Jensen, N.G.
1998-12-31
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Using nonlinear techniques and large-scale simulations, we have systematically studied meso-scale pattern formation and dynamics in nonlinear, nonequilibrium systems exhibiting topological excitations (dislocations, vortices, vortex lines, domain walls); dislocation generation from crack fronts in ductile materials; the smoothing of rough surfaces in solid-on-solid models; ordering and melting of moving flux lattices in three-dimensional Josephson junction arrays with external magnetic field, current, and disorder; filamentary and plastic vortex flow in disordered thin films superconductors; magnetic vortices in Heisenberg spin layers; and hierarchical twinning and tweed texture in elastic models.
Fisher information for the position-dependent mass Schrödinger system
NASA Astrophysics Data System (ADS)
Falaye, B. J.; Serrano, F. A.; Dong, Shi-Hai
2016-01-01
This study presents the Fisher information for the position-dependent mass Schrödinger equation with hyperbolic potential V (x) = -V0csch2 (ax). The analysis of the quantum-mechanical probability for the ground and exited states (n = 0, 1, 2) has been obtained via the Fisher information. This controls both chemical and physical properties of some molecular systems. The Fisher information is considered only for x > 0 due to the singular point at x = 0. We found that Fisher-information-based uncertainty relation and the Cramer-Rao inequality holds. Some relevant numerical results are presented. The results presented show that the Cramer-Rao and the Heisenberg products in both spaces provide a natural measure for anharmonicity of -V0csch2 (ax).
Numerical simulations of strongly correlated electron and spin systems
NASA Astrophysics Data System (ADS)
Changlani, Hitesh Jaiprakash
Developing analytical and numerical tools for strongly correlated systems is a central challenge for the condensed matter physics community. In the absence of exact solutions and controlled analytical approximations, numerical techniques have often contributed to our understanding of these systems. Exact Diagonalization (ED) requires the storage of at least two vectors the size of the Hilbert space under consideration (which grows exponentially with system size) which makes it affordable only for small systems. The Density Matrix Renormalization Group (DMRG) uses an intelligent Hilbert space truncation procedure to significantly reduce this cost, but in its present formulation is limited to quasi-1D systems. Quantum Monte Carlo (QMC) maps the Schrodinger equation to the diffusion equation (in imaginary time) and only samples the eigenvector over time, thereby avoiding the memory limitation. However, the stochasticity involved in the method gives rise to the "sign problem" characteristic of fermion and frustrated spin systems. The first part of this thesis is an effort to make progress in the development of a numerical technique which overcomes the above mentioned problems. We consider novel variational wavefunctions, christened "Correlator Product States" (CPS), that have a general functional form which hopes to capture essential correlations in the ground states of spin and fermion systems in any dimension. We also consider a recent proposal to modify projector (Green's Function) Quantum Monte Carlo to ameliorate the sign problem for realistic and model Hamiltonians (such as the Hubbard model). This exploration led to our own set of improvements, primarily a semistochastic formulation of projector Quantum Monte Carlo. Despite their limitations, existing numerical techniques can yield physical insights into a wide variety of problems. The second part of this thesis considers one such numerical technique - DMRG - and adapts it to study the Heisenberg antiferromagnet
Statistical Mechanics of Quantum Integrable Systems
NASA Astrophysics Data System (ADS)
Wadati, Miki; Kato, Go; Iida, Toshiaki
Recent developments in statistical mechanics of quantum integrable systems are reviewed. Those studies are fundamental and have a renewed interest related to newly developing fields such as atomic Bose-Einstein condensations, photonic crystals and quantum computations. After a brief summary of the basic concepts and methods, the following three topics are discussed. First, by the thermal Bethe ansatz (TBA), a hard-core Bose gas is exactly solved. The model includes fully the effect of excluded volume and is identified to be a c=1 conformal field theory. Second, the cluster expansion method based on the periodic boundary condition for the Bethe wave function, which we call the Bethe ansatz cluster expansion (BACE) method, is developed for a δ-function gas and the XXX Heisenberg chain. This directly proves the TBA and reveals intrinsic properties of quantum integrable systems. Third, for a δ-function gas, the integral equations for the distribution functions of the quasi-momentum and the quasi-particle energy are solved in the form of power series. In the weak coupling case, the results reproduce those of Bogoliubov theory.
Shumilin, A V
2016-10-01
We discuss the spin excitations in systems with hopping electron conduction and strong position disorder. We focus on the problem in a strong magnetic field when the spin Hamiltonian can be reduced to the effective single-particle Hamiltonian and treated with conventional numerical technics. It is shown that in a 3D system with Heisenberg exchange interaction the spin excitations have a delocalized part of the spectrum even in the limit of strong disorder, thus leading to the possibility of the coherent spin transport. The spin transport provided by the delocalized excitations can be described by a diffusion coefficient. Non-homogenous magnetic fields lead to the Anderson localization of spin excitations while anisotropy of the exchange interaction results in the Lifshitz localization of excitations. We discuss the possible effect of the additional exchange-driven spin diffusion on the organic spin-valve devices. PMID:27484892
NASA Astrophysics Data System (ADS)
Shumilin, A. V.
2016-10-01
We discuss the spin excitations in systems with hopping electron conduction and strong position disorder. We focus on the problem in a strong magnetic field when the spin Hamiltonian can be reduced to the effective single-particle Hamiltonian and treated with conventional numerical technics. It is shown that in a 3D system with Heisenberg exchange interaction the spin excitations have a delocalized part of the spectrum even in the limit of strong disorder, thus leading to the possibility of the coherent spin transport. The spin transport provided by the delocalized excitations can be described by a diffusion coefficient. Non-homogenous magnetic fields lead to the Anderson localization of spin excitations while anisotropy of the exchange interaction results in the Lifshitz localization of excitations. We discuss the possible effect of the additional exchange-driven spin diffusion on the organic spin-valve devices.
2015-01-01
A method to separate the effects of Heisenberg spin exchange (HSE) and dipole–dipole (DD) interactions on EPR spectra of nitroxide spin probes in solution by employing 15N and 14N nitroxide spin probes in parallel experiments is developed theoretically and tested experimentally. Comprehensive EPR measurements are reported of 4-oxo-2,2,6,6-tetramethylpiperidine-d16;1-15N-1-oxyl (perdeuterated 15N Tempone; 15pDT), in 70 wt % aqueous glycerol as functions of concentration and temperature. The method, termed the relative broadening constant method (RBCM), is demonstrated by using the present results together with those in the literature that employed perdeuterated 14N Tempone (14pDT) under identical conditions. In principle, the separation of DD and HSE is dependent on the model of diffusion and molecular-kinetic parameters; however, within present day experimental uncertainties, the RBCM method turns out to be insensitive to the model. The earlier methods to separate DD and HSE by measuring the dispersion component introduced by the two interactions shows general agreement with the RBCM; however, there are discrepancies larger than estimated uncertainties due to random errors. Thus, further support is found for Salikhov’s recent theory of the effects of DD and HSE on EPR spectra (Appl. Magn. Reson.2010, 38, 237); however, detailed confirmation is still lacking. The RBCM affords a possible approach to separate HSE and DD in spectra complicated by slow motion and/or overlap with other resonance lines, allowing the method to be used in situations more complicated than low-viscosity simple liquids. PMID:25035905
Scar and antiscar quantum effects in open chaotic systems.
Kaplan, L
1999-05-01
We predict and numerically observe strong periodic orbit effects in the properties of weakly open quantum systems with a chaotic classical limit. Antiscars lead to a large number of exponentially narrow isolated resonances when the single-channel (or tunneling) opening is located on a short unstable orbit of the closed system; the probability to remain in the system at long times is thus exponentially enhanced over the random matrix theory prediction. The distribution of resonance widths and the probability to remain are quantitatively given in terms of only the stability matrix of the orbit on which the opening is placed. The long-time remaining probability density is nontrivially distributed over the available phase space; it can be enhanced or suppressed near orbits other than the one on which the lead is located, depending on the periods and classical actions of these other orbits. These effects of the short periodic orbits on quantum decay rates have no classical counterpart, and first appear on times scales much larger than the Heisenberg time of the system. All the predictions are quantitatively compared with numerical data. PMID:11969492
Pulsed field magnetization in rare-earth kagome systems
NASA Astrophysics Data System (ADS)
Hoch, M. J. R.; Zhou, H. D.; Mun, E.; Harrison, N.
2016-02-01
The rare-earth kagome systems R 3Ga5SiO14 (R = Nd or Pr) exhibit cooperative paramagnetism at low temperatures. Evidence for correlated spin clusters in these weakly frustrated systems has previously been obtained from neutron scattering and from ESR and NMR results. The present pulsed field (0-60 T, 25 ms) magnetization measurements made on single crystals of Nd3Ga5SiO14 (NGS) and Pr3Ga5SiO14 (PGS) at temperatures down to 450 mK have revealed striking differences in the magnetic responses of the two materials. For NGS the magnetization shows a low field plateau, saturation in high transient fields, and significant hysteresis while the PGS magnetization does not saturate in transient fields up to 60 T and shows no hysteresis or plateaus. Nd3+ is a Kramers ion while Pr3+ is a non-Kramers ion and the crystal field effects are quite different in the two systems. For the conditions used in the experiments the magnetization behavior is not in agreement with Heisenberg model predictions for kagome systems in which easy-axis anisotropy is much larger than the exchange coupling. The extremely slow spin dynamics found below 4 K in NGS is, however, consistent with the model for Kramers ions and provides a basis for explaining the pulsed field magnetization features.
Pulsed field magnetization in rare-earth kagome systems.
Hoch, M J R; Zhou, H D; Mun, E; Harrison, N
2016-02-01
The rare-earth kagome systems R 3Ga5SiO14 (R = Nd or Pr) exhibit cooperative paramagnetism at low temperatures. Evidence for correlated spin clusters in these weakly frustrated systems has previously been obtained from neutron scattering and from ESR and NMR results. The present pulsed field (0-60 T, 25 ms) magnetization measurements made on single crystals of Nd3Ga5SiO14 (NGS) and Pr3Ga5SiO14 (PGS) at temperatures down to 450 mK have revealed striking differences in the magnetic responses of the two materials. For NGS the magnetization shows a low field plateau, saturation in high transient fields, and significant hysteresis while the PGS magnetization does not saturate in transient fields up to 60 T and shows no hysteresis or plateaus. Nd(3+) is a Kramers ion while Pr(3+) is a non-Kramers ion and the crystal field effects are quite different in the two systems. For the conditions used in the experiments the magnetization behavior is not in agreement with Heisenberg model predictions for kagome systems in which easy-axis anisotropy is much larger than the exchange coupling. The extremely slow spin dynamics found below 4 K in NGS is, however, consistent with the model for Kramers ions and provides a basis for explaining the pulsed field magnetization features. PMID:26732305
NASA Astrophysics Data System (ADS)
Asimakopoulos, Aristotelis
While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution. Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty
Dissipation equation of motion approach to open quantum systems
NASA Astrophysics Data System (ADS)
Yan, YiJing; Jin, Jinshuang; Xu, Rui-Xue; Zheng, Xiao
2016-08-01
This paper presents a comprehensive account of the dissipaton-equation-of-motion (DEOM) theory for open quantum systems. This newly developed theory treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that are also experimentally measurable. Despite the fact that DEOM recovers the celebrated hierarchical-equations-of-motion (HEOM) formalism, these two approaches have some fundamental differences. To show these differences, we also scrutinize the HEOM construction via its root at the influence functional path integral formalism. We conclude that many unique features of DEOM are beyond the reach of the HEOM framework. The new DEOM approach renders a statistical quasi-particle picture to account for the environment, which can be either bosonic or fermionic. The review covers the DEOM construction, the physical meanings of dynamical variables, the underlying theorems and dissipaton algebra, and recent numerical advancements for efficient DEOM evaluations of various problems. We also address the issue of high-order many-dissipaton truncations with respect to the invariance principle of quantum mechanics of Schrödinger versus Heisenberg prescriptions. DEOM serves as a universal tool for characterizing of stationary and dynamic properties of system-and-bath interferences, as highlighted with its real-time evaluation of both linear and nonlinear current noise spectra of nonequilibrium electronic transport.
Spectral Theory for Interacting Particle Systems Solvable by Coordinate Bethe Ansatz
NASA Astrophysics Data System (ADS)
Borodin, Alexei; Corwin, Ivan; Petrov, Leonid; Sasamoto, Tomohiro
2015-11-01
We develop spectral theory for the q-Hahn stochastic particle system introduced recently by Povolotsky. That is, we establish a Plancherel type isomorphism result that implies completeness and biorthogonality statements for the Bethe ansatz eigenfunctions of the system. Owing to a Markov duality with the q-Hahn TASEP (a discrete-time generalization of TASEP with particles' jump distribution being the orthogonality weight for the classical q-Hahn orthogonal polynomials), we write down moment formulas that characterize the fixed time distribution of the q-Hahn TASEP with general initial data. The Bethe ansatz eigenfunctions of the q-Hahn system degenerate into eigenfunctions of other (not necessarily stochastic) interacting particle systems solvable by the coordinate Bethe ansatz. This includes the ASEP, the (asymmetric) six-vertex model, and the Heisenberg XXZ spin chain (all models are on the infinite lattice). In this way, each of the latter systems possesses a spectral theory, too. In particular, biorthogonality of the ASEP eigenfunctions, which follows from the corresponding q-Hahn statement, implies symmetrization identities of Tracy and Widom (for ASEP with either step or step Bernoulli initial configuration) as corollaries. Another degeneration takes the q-Hahn system to the q-Boson particle system (dual to q-TASEP) studied in detail in our previous paper (2013). Thus, at the spectral theory level we unify two discrete-space regularizations of the Kardar-Parisi-Zhang equation/stochastic heat equation, namely, q-TASEP and ASEP.
Composite system in deformed space with minimal length
NASA Astrophysics Data System (ADS)
Quesne, C.; Tkachuk, V. M.
2010-01-01
For composite systems made of N different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first order in the deformation parameters. Such operators satisfy the deformed algebra with effective deformation parameters. As a consequence, a two-particle system can be reduced to a one-particle problem for the internal motion. As an example, the correction to the hydrogen atom nS energy levels is re-evaluated. Comparison with high-precision experimental data leads to an upper bound of the minimal length for the electron equal to 3.3×10-18m. The effective Hamiltonian describing the center-of-mass motion of a macroscopic body in an external potential is also found. For such a motion, the effective deformation parameter is substantially reduced due to a factor 1/N2. This explains the strangely small result previously obtained for the minimal length from a comparison with the observed precession of the perihelion of Mercury. From our study, an upper bound of the minimal length for quarks equal to 2.4×10-17m is deduced, which appears close to that obtained for electrons.
Boundary driven open quantum many-body systems
Prosen, Tomaž
2014-01-08
In this lecture course I outline a simple paradigm of non-eqjuilibrium quantum statistical physics, namely we shall study quantum lattice systems with local, Hamiltonian (conservative) interactions which are coupled to the environment via incoherent processes only at the system's boundaries. This is arguably the simplest nontrivial context where one can study far from equilibrium steady states and their transport properties. We shall formulate the problem in terms of a many-body Markovian master equation (the so-called Lindblad equation, and some of its extensions, e.g. the Redfield eqaution). The lecture course consists of two main parts: Firstly, and most extensively we shall present canonical Liouville-space many-body formalism, the so-called 'third quantization' and show how it can be implemented to solve bi-linear open many-particle problems, the key peradigmatic examples being the XY spin 1/2 chains or quasi-free bosonic (or harmonic) chains. Secondly, we shall outline several recent approaches on how to approach exactly solvable open quantum interacting many-body problems, such as anisotropic Heisenberg ((XXZ) spin chain or fermionic Hubbard chain.
Generalization of Luttinger's Theorem for Fermionic Ladder Systems
NASA Astrophysics Data System (ADS)
Gagliardini, P.; Haas, S.; Rice, T. M.; Sigrist, M.
1998-03-01
Recently Yamanaka et al.(M. Yamanaka, M. Oshikawa, and I. Affleck, PRL 79), 1110 (1997). adapted the Lieb-Schultz-Mattis theorem to obtain a non-perturbative generalization of Luttinger's theorem for 1-dim. fermionic systems. Their method can be extended to ladder systems. The key quantity which enters in a Hubbard or t-J model is the sum of the electron occupation numbers on a rung. At half-filling, this leads at once to a proof that undoped Heisenberg ladders have gapless excitations when the number of legs is odd. Upon doping, the Fermi wavevectors of individual channels are not conserved under interaction, but their sum is. This result does not require a Fermi surface in each channel and is consistent with the recently proposed assignment of 1 el. per rung to gapped insulating even-parity channels, and 1-δ els. to a Luttinger liquid in the odd-parity channel in a lightly doped 3-leg ladder (δ: hole doping). The crossover to 2 dim. occurs in the limit of a large number of legs, and it is the area enclosed by the Fermi surface which enters, consistent with Luttinger's theorem for the case of Landau Fermi liquids.
Enumerative Geometry, Tau-Functions and Heisenberg-Virasoro Algebra
NASA Astrophysics Data System (ADS)
Alexandrov, A.
2015-08-01
In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich-Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the tau-functions in terms of matrix integrals, Virasoro constraints and Kac-Schwarz operators. All constructed operators belong to the algebra (or group) of symmetries of the KP hierarchy.
The Heisenberg Uncertainty Principle Demonstrated with An Electron Diffraction Experiment
ERIC Educational Resources Information Center
Matteucci, Giorgio; Ferrari, Loris; Migliori, Andrea
2010-01-01
An experiment analogous to the classical diffraction of light from a circular aperture has been realized with electrons. The results are used to introduce undergraduate students to the wave behaviour of electrons. The diffraction fringes produced by the circular aperture are compared to those predicted by quantum mechanics and are exploited to…
Entangling the lattice clock: Towards Heisenberg-limited timekeeping
Weinstein, Jonathan D.; Beloy, Kyle; Derevianko, Andrei
2010-03-15
A scheme is presented for entangling the atoms of an optical lattice to reduce the quantum projection noise of a clock measurement. The divalent clock atoms are held in a lattice at a 'magic' wavelength that does not perturb the clock frequency - to maintain clock accuracy - while an open-shell J=1/2 'head' atom is coherently transported between lattice sites via the lattice polarization. This polarization-dependent 'Archimedes' screw' transport at magic wavelength takes advantage of the vanishing vector polarizability of the scalar, J=0, clock states of bosonic isotopes of divalent atoms. The on-site interactions between the clock atoms and the head atom are used to engineer entanglement and for clock readout.
Quantum Fractals: From Heisenberg's Uncertainty to Barnsley's Fractality
NASA Astrophysics Data System (ADS)
Jadczyk, Arkadiusz
2014-07-01
This book brings together two concepts. The first is over a hundred years old -- the "quantum", while the second, "fractals", is newer, achieving popularity after the pioneering work of Benoit Mandelbrot. Both areas of research are expanding dramatically day by day. It is somewhat amazing that quantum theory, in spite of its age, is still a boiling mystery as we see in some quotes from recent publications addressed to non-expert readers:...
Generalized Heisenberg algebras and k-generalized Fibonacci numbers
NASA Astrophysics Data System (ADS)
Schork, Matthias
2007-04-01
It is shown how some of the recent results of de Souza et al (2006 J. Phys. A: Math. Gen. 39 10415) can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al correspond to k = 2.
The quantum-classical crossover in the adiabatic response of chaotic systems
NASA Astrophysics Data System (ADS)
Auslaender, Ophir M.; Fishman, Shmuel
2000-03-01
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins, Wilkinson and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is often proportional to the rate of energy transfer between the systems. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite-time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall-off is inversely proportional to time for the Gaussian orthogonal ensemble. The correlation function is found to be dominated by the nearest-neighbour level spacings. It was calculated for a variety of nearest-neighbour level spacing distributions, including ones that do not originate from RMT ensembles. The various approximate formulae obtained are tested numerically in RMT. The results shed light on the quantum to classical crossover for chaotic systems. The implications on the possibility to experimentally observe deterministic friction are discussed.
Introduction to the Statistical Physics of Integrable Many-body Systems
NASA Astrophysics Data System (ADS)
Šamaj, Ladislav Å.; Bajnok, Zoltán
2013-05-01
Preface; Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index.
Study of ultrasonic attenuation for the Kondo and magnetic effects in heavy fermion systems
NASA Astrophysics Data System (ADS)
Baral, Purna Chandra; Rout, Govind Chandra
2013-05-01
The heavy fermion (HF) systems draw considerable attention due to their cooperative phenomena and anomalous properties arising out of the huge effective mass. A heavy fermion system is described by a model Hamiltonian consisting of the Kondo lattice model in addition to the Heisenberg-type spin-spin interaction among the localised electrons. The Hamiltonian is treated in the mean-field approximation to find the Kondo singlet parameter λ and the short-ranged f-electron correlation parameter Γ. In order to investigate ultrasonic absorption in the system, we consider the phonon interaction with the bare f-electrons, and the phonon coupling to the Kondo singlets. Further, the phonon Hamiltonian is considered in the harmonic approximation. The phonon Green's function is calculated in closed form. The imaginary part of the phonon self-energy describes the ultrasonic attenuation for the HF systems. The calculated ultrasonic attenuation clearly displays the f-electron correlation region separated by the Kondo singlet state at low temperatures. The correlation transition temperature and the Kondo temperature are located at dips in the temperature-dependent ultrasonic attenuation. The parameter dependence of the attenuation is investigated by varying the physical parameters of the HF systems and the wave frequency, and the experimental observations are explained on the basis of the model calculations.
Feasibility of a metamagnetic transition in correlated systems.
Acharya, Swagata; Medhi, Amal; Vidhyadhiraja, N S; Taraphder, A
2016-03-23
The long-standing issue of the competition between the magnetic field and the Kondo effect, favoring, respectively, triplet and singlet ground states, is addressed using a cluster slave-rotor mean-field theory for the Hubbard model and its spin-correlated, spin-frustrated extensions in two dimensions. The metamagnetic jump is established and compared with earlier results of dynamical mean-field theory. This approach also reproduces the emergent super-exchange energy scale in the insulating side. A scaling is found for the critical Zeeman field in terms of the intrinsic coherence scale just below the metal-insulator transition, where the critical spin fluctuations are soft. The conditions required for metamagnetism to appear at a reasonable field are also underlined. Gutzwiller analysis on the two-dimensional Hubbard model and a quantum Monte Carlo calculation on the Heisenberg spin system are performed to check the limiting cases of the cluster slave-rotor results for the Hubbard model. Low-field scaling features for magnetization are discussed. PMID:26895399
Feasibility of a metamagnetic transition in correlated systems
NASA Astrophysics Data System (ADS)
Acharya, Swagata; Medhi, Amal; Vidhyadhiraja, N. S.; Taraphder, A.
2016-03-01
The long-standing issue of the competition between the magnetic field and the Kondo effect, favoring, respectively, triplet and singlet ground states, is addressed using a cluster slave-rotor mean-field theory for the Hubbard model and its spin-correlated, spin-frustrated extensions in two dimensions. The metamagnetic jump is established and compared with earlier results of dynamical mean-field theory. This approach also reproduces the emergent super-exchange energy scale in the insulating side. A scaling is found for the critical Zeeman field in terms of the intrinsic coherence scale just below the metal-insulator transition, where the critical spin fluctuations are soft. The conditions required for metamagnetism to appear at a reasonable field are also underlined. Gutzwiller analysis on the two-dimensional Hubbard model and a quantum Monte Carlo calculation on the Heisenberg spin system are performed to check the limiting cases of the cluster slave-rotor results for the Hubbard model. Low-field scaling features for magnetization are discussed.
NASA Astrophysics Data System (ADS)
Young, A. Peter
2009-03-01
Systems with disorder and ``frustration'' occur in many branches of science. There has been considerable effort to understand one such type of system, known as the ``spin glass'', because it can be probed in fine detail experimentally by applying a magnetic field, and because it can be modeled by simple-looking Hamiltonians which are amenable to numerical simulation. Analytical work is very difficult and has been carried out mainly on models with unphysical features such as infinite-range interactions. Hence, much of what we know about spin glasses and related systems comes from numerical simulations on simplified models. In this talk I will describe some of the difficulties in performing reliable spin glass simulations. Then I will discuss several questions concerning phase transitions in spin glasses and related systems that have been addressed by simulations in recent years including (i) whether there is universality, (ii) whether there is a ``vortex glass'' transition in a disordered type-II superconductor in a magnetic field, (iii) whether ``chiralities'' play a crucial role in Heisenberg spin glasses, and (iv) whether there is a line of transitions (AT line) in a magnetic field.
Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I.; Verrucchi, Paola
2013-01-01
The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables , and broadened according to their quantum probability distribution. Such distribution is independent of φ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because φ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field. PMID:23572581
Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I; Verrucchi, Paola
2013-04-23
The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the s = 1/2 Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables (θ, ϕ), and broadened according to their quantum probability distribution. Such distribution is independent of ϕ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because ϕ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field.
Thermodynamics of bipartite systems: Application to light-matter interactions
Boukobza, E.; Tannor, D. J.
2006-12-15
Heat and work for quantum systems governed by dissipative master equations with a time-dependent driving field were introduced in the pioneering work of Alicki [J. Phys. A 12, L103 (1979)]. Alicki's work was in the Schroedinger picture; here we extend these definitions to the Heisenberg and interaction pictures. We show that, in order to avoid consistency problems, the full time derivatives in the definitions for heat flux and power (work flux) should be replaced by partial time derivatives. We also present an alternative approach to the partitioning of the energy flux which differs from that of Alicki in that the instantaneous interaction energy with the external field is not included directly. We then proceed to generalize Alicki's definition of power by replacing the original system and its external driving field with a larger, bipartite system, governed by a time-independent Hamiltonian. Using the definition of heat flux and the generalized definition of power, we derive the first law of thermodynamics in differential form, for both the full bipartite system and the partially traced subsystems. Although the second law (Clausius formulation) is satisfied for the full bipartite system, we find that in general there is no rigorous formulation of the second law for the partially traced subsystem unless certain additional requirements are met. Once these requirements are satisfied, however, both the Carnot and the Clausius formulations of the second law are satisfied. We illustrate this thermodynamic analysis on both the simple Jaynes-Cummings model and an extended dissipative Jaynes-Cummings model, which is a model for a quantum amplifier.
Properties of the low dimensional Sr2Cu(W1-xMox)O6 spin system
NASA Astrophysics Data System (ADS)
Chmaissem, Omar; Avdeev, Maxim; Danilkin, Sergey; Vasala, Sami; Yamauchi, Hisao; Karppinen, Maarit
2015-03-01
Low-dimensional spin systems have gained much attention in solid state physics. Such systems could have a ground state with no long-range magnetic order and an energy gap in the spin excitation spectrum, offering the possibility of a quantum spin-liquid phase. Quantum fluctuations causing the spin-liquid state are particularly strong in systems with reduced dimensionality and a low spin value; and magnetic frustration can further enhance the fluctuations. Among various low-dimensional spin systems, the S = 1/2 Heisenberg frustrated square lattice model is especially interesting due to its relevance to high-TC superconducting cuprates, whose undoped parent materials are S = 1/2 square-lattice antiferromagnets. Sr2CuWO6andSr2CuMoO6 have been found to be quasi-two-dimensional S = 1/2 magnetic systems with a square lattice of Cu-ions. These compounds show low-dimensional magnetic properties, with no clear indication of long-range order in magnetic susceptibility. I will discuss the materials properties and the observation of long range magnetism by neutron diffraction and other techniques. SV and MK acknowledge financial support by Academy of Finland (No. 255562) and OC by the U.S. Department of Energy, Office of Science, Materials Sciences and Engineering Division.
Frustration and chiral orderings in correlated electron systems.
Batista, Cristian D; Lin, Shi-Zeng; Hayami, Satoru; Kamiya, Yoshitomo
2016-08-01
The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S = 1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.
Frustration and chiral orderings in correlated electron systems.
Batista, Cristian D; Lin, Shi-Zeng; Hayami, Satoru; Kamiya, Yoshitomo
2016-08-01
The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S = 1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect. PMID:27376461
Frustration and chiral orderings in correlated electron systems
NASA Astrophysics Data System (ADS)
Batista, Cristian D.; Lin, Shi-Zeng; Hayami, Satoru; Kamiya, Yoshitomo
2016-08-01
The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson’s proposal of a quantum spin liquid ground state for a two-dimensional lattice S = 1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.
Yasui, Yukio; Kawamura, Yuji; Kobayashi, Yoshiaki; Sato, Masatoshi
2014-05-07
Magnetic susceptibility χ, specific heat C, capacitance C{sub p}, and {sup 23}Na-NMR measurements have been carried out on polycrystalline samples of quantum spin linear trimer system Na{sub 2}Cu{sub 3}Ge{sub 4}O{sub 12}, which has the one-dimensional array of Cu{sub 3}O{sub 8} trimers formed of edge-sharing three CuO{sub 4} square planes. The exchange interactions between the Cu{sup 2+} (S = 1/2) spins have been determined by analyzing χ-T and C-T curves. By employing the isolated S = 1/2 Heisenberg trimer model above 70 K, the nearest-neighbor exchange couplings J{sub 1} and the second-neighbor one J{sub 2} in trimer have been evaluated to J{sub 1}/k{sub B} = 30 ± 20 K (antiferromagnetic) and J{sub 2}/k{sub B} = 340 ± 20 K. At low temperature region, two spins of the edge in the Cu{sub 3}O{sub 8} trimers form a nonmagnetic singlet by strong antiferromagnetic interaction J{sub 2}, and the spin left in the center of the Cu{sub 3}O{sub 8} trimer forms one-dimensional chains by the exchange interaction J{sub 3} between the trimers. By employing the S = 1/2 uniform Heisenberg chain model below 70 K, we have evaluated to J{sub 3}/k{sub B} = 18 ± 1 K. The mechanism of multiferroic behavior at T{sub c} = 2 K is discussed.
Marquette, Ian; Quesne, Christiane
2015-06-15
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.
NASA Astrophysics Data System (ADS)
Specht, Judith; Verdenhalven, Eike; Theuerholz, Sverre; Knorr, Andreas; Richter, Marten
2016-03-01
We derive a theoretical framework for describing hybrid organic-inorganic systems consisting of an ordered organic molecular layer coupled to a semiconductor quantum well (e.g., ZnO). A Heisenberg equation of motion technique based on a density matrix formalism is applied to derive dynamical equations for the composite system on a mesoscopic scale. Our theoretical approach focuses on the inuence of nonradiative Förster excitation transfer across the hybrid interface on linear optical absorption spectra. Therefore, the dielectric screening is discussed at the interface of two materials with different dielectric constants. Moreover, the Förster transfer matrix element is calculated in the point-dipole approximation. For a consistent theoretical description of both constituents (i.e., the molecular layer and the semiconductor substrate), the problem is treated in momentum space. Solving the equations of motion for the microscopic polarizations in frequency space directly leads to an equation for the frequency-dependent linear absorption coefficient. Our theoretical approach forms the basis for studying parameter regimes and geometries with optimized excitation transfer efficiency across the semiconductor/ molecule interface.
The Doppler Effect based acoustic source separation for a wayside train bearing monitoring system
NASA Astrophysics Data System (ADS)
Zhang, Haibin; Zhang, Shangbin; He, Qingbo; Kong, Fanrang
2016-01-01
Wayside acoustic condition monitoring and fault diagnosis for train bearings depend on acquired acoustic signals, which consist of mixed signals from different train bearings with obvious Doppler distortion as well as background noises. This study proposes a novel scheme to overcome the difficulties, especially the multi-source problem in wayside acoustic diagnosis system. In the method, a time-frequency data fusion (TFDF) strategy is applied to weaken the Heisenberg's uncertainty limit for a signal's time-frequency distribution (TFD) of high resolution. Due to the Doppler Effect, the signals from different bearings have different time centers even with the same frequency. A Doppler feature matching search (DFMS) algorithm is then put forward to locate the time centers of different bearings in the TFD spectrogram. With the determined time centers, time-frequency filters (TFF) are designed with thresholds to separate the acoustic signals in the time-frequency domain. Then the inverse STFT (ISTFT) is taken and the signals are recovered and filtered aiming at each sound source. Subsequently, a dynamical resampling method is utilized to remove the Doppler Effect. Finally, accurate diagnosis for train bearing faults can be achieved by applying conventional spectrum analysis techniques to the resampled data. The performance of the proposed method is verified by both simulated and experimental cases. It shows that it is effective to detect and diagnose multiple defective bearings even though they produce multi-source acoustic signals.
Investigating non-Markovian dynamics of quantum open systems
NASA Astrophysics Data System (ADS)
Chen, Yusui
-qubit systems and multilevel systems. Based on our systematic method, we also show how to solve different types of models. In the last part, we use Heisenberg equations of motion and quantum trajectory approach to obtain the exact master equation for a quantum harmonic oscillator chains coupled to two finite temperature environments. The derived exact non-Markovian master equation is useful for exploration of quantum transport and quantum coherence dynamics.
Non-equilibrium Aspects of Quantum Integrable Systems
NASA Astrophysics Data System (ADS)
Andrei, Natan
The study of non-equilibrium dynamics of interacting many body systems is currently one of the main challenges of modern condensed matter physics, driven by the spectacular progress in the ability to create experimental systems - trapped cold atomic gases are a prime example - that can be isolated from their environment and be highly controlled. Many old and new questions can be addressed: thermalization of isolated systems, nonequilibrium steady states, the interplay between non equilibrium currents and strong correlations, quantum phase transitions in time, universality among others. In this talk I will describe nonequilibrium quench dynamics in integrable quantum systems. I'll discuss the time evolution of the Lieb-Liniger system, a gas of interacting bosons moving on the continuous infinite line and interacting via a short range potential. Considering a finite number of bosons on the line we find that for any value of repulsive coupling the system asymptotes towards a strongly repulsive gas for any initial state, while for an attractive coupling, the system forms a maximal bound state that dominates at longer times. In the thermodynamic limit -with the number of bosons and the system size sent to infinity at a constant density and the long time limit taken subsequently- I'll show that the density and density-density correlation functions for strong but finite positive coupling are described by GGE for translationally invariant initial states with short range correlations. As examples I'll discuss quenches from a Mott insulator initial state or a Newton's Cradle. Then I will show that if the initial state is strongly non translational invariant, e.g. a domain wall configuration, the system does not equilibrate but evolves into a nonequilibrium steady state (NESS). A related NESS arises when the quench consists of coupling a quantum dot to two leads held at different chemical potential, leading in the long time limit to a steady state current. Time permitting I
NASA Astrophysics Data System (ADS)
Leahy, Ian; Bornstein, Alex; Choi, Kwang-Yong; Lee, Minhyea
α -RuCl3, a quasi -two-dimensional honeycomb lattice is known to be a candidate material to realize the Heisenberg-Kitaev spin model of a highly anisotropic bond-dependent exchange interaction. We investigate in-plane thermal conductivity (κ) as a function of temperature (T) and in-plane applied field (H). At H = 0 , the onset of a strong increase in κ marks the spontaneous long range ordering temperature, Tc = 6 . 5 K , corresponding to ``zigzag'' antiferromagnetic ordering. A broad peak appearing below Tc in κ was found to be suppressed significantly as H increases up to ~ 7 T , implying the system undergoes a field-induced transition from ordered to a new spin-disordered state analogous to the transverse-field Ising model. Further increasing H above 7 . 1 T , the large field seems to begin polarizing spins thus increasing the phonon mean free path, resulting in a significant rise in κ. This tendency is clearly shown in the field dependence of κ below Tc, which has a pronounced minimum at Hmin = 7 . 1 T . We will discuss our scaling analysis to characterize this field-induced phase transition and compare to the transverse-field Ising spin system. Work at the University of Colorado was supported by the US DOE Basic Energy Sciences under Award No. DE-SC0006888.
Entanglement dynamics of one-dimensional driven spin systems in time-varying magnetic fields
Alkurtass, Bedoor; Sadiek, Gehad; Kais, Sabre
2011-08-15
We study the dynamics of nearest-neighbor entanglement for a one-dimensional spin chain with a nearest-neighbor time-dependent Heisenberg coupling J(t) between the spins in the presence of a time-dependent external magnetic field h(t) at zero and finite temperatures. We consider different forms of time dependence for the coupling and magnetic field: exponential, hyperbolic, and periodic. Solving the system numerically, we examined the system-size effect on the entanglement asymptotic value. It was found that, for a small system size, the entanglement starts to fluctuate within a short period of time after applying the time-dependent coupling. The period of time increases as the system size increases and disappears completely as the size goes to infinity. Testing the effect of the transition constant for an exponential or hyperbolic coupling showed a direct impact on the asymptotic value of the entanglement; the larger the constant is, the lower the asymptotic value and the more rapid decay of entanglement are, which confirms the nonergodic character of the system. We also found that, when J(t) is periodic, the entanglement shows a periodic behavior with the same period, which disappears upon applying periodic magnetic field with the same frequency. Solving the case J(t)={lambda}h(t), for constant {lambda}, exactly, we showed that the time evolution and asymptotic value of entanglement are dictated solely by the parameter {lambda}=J/h rather than the individual values of J and h, not only when they are time independent and at zero temperature, but also when they are time dependent but proportional at zero and finite temperatures for all degrees of anisotropy.
Physics of frustrated systems: A neutron scattering study
NASA Astrophysics Data System (ADS)
Gasparovic, Goran
Frustration refers to the inability of a system to simultaneously satisfy all interactions. The principal ingredients of frustration are (i) competition between interactions within the system, and (ii) conflicting constraints established by symmetry, or higher energy interactions. The behavior of frustrated systems is generally difficult to predict, and often results in novel cooperative states and phenomena. Frustration is common in disordered systems, in this dissertation, however, we focus on frustrated systems without quenched disorder. Effects of frustration tend to be pronounced when coupled with weak connectivity. Weak connectivity refers to a topology in which the order in one part of the system does not constrain the order in other parts. We have used neutron scattering to study structurally and magnetically frustrated systems, both strongly and weakly connected. In ZrW2O8 and Sc2(WO4) 3, anomalously large Negative Thermal Expansion (NTE) has been observed over a wide temperature range. Analysis indicates that the NTE effect in these materials is driven by folding of rigid units consisting of strongly bonded oxygen-metal polyhedra. Weak connectivity is manifested by structural under-constraint, which enables soft optical phonons. Using neutron scattering, we observed an unusually high density-of-states at low energies, and mapped the dispersion relations of the most intense phonon modes. While in conventional materials soft phonon modes typically signal an imminent structural phase transition, in NTE materials the transition is frustrated by the incompatibility between the crystal symmetry and the symmetry of the soft phonon modes. This results in the unusual NTE effect. RbFe(MoO4)2 is a frustrated, quasi-classical ( S = 5/2), quasi-two-dimensional Heisenberg antiferromagnet on a triangular lattice, with easy-plane anisotropy. In RbFe(MoO4)2, frustrated units (triangles) share edges, and are strongly connected. Although a long range magnetic order is
NASA Astrophysics Data System (ADS)
Babadi, Mehrtash; Demler, Eugene; Knap, Michael
2015-10-01
We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-1 /2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1 /N expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild et al., Phys. Rev. Lett. 113, 147205 (2014), 10.1103/PhysRevLett.113.147205].
NASA Astrophysics Data System (ADS)
Han, Tianheng
New physics, such as a quantum spin liquid, can emerge in systems where quantum fluctuations are enhanced due to reduced dimensionality and strong frustration . The realization of a quantum spin liquid in two-dimensions would represent a new state of matter. It is believed that spin liquid physics plays a role in the phenomenon of high-Tc superconductivity, and the topological properties of the spin liquid state may have applications in the field of quantum information. The Zn-paratacamite family, ZnxCu4-- x(OH)6Cl2 for x > 0.33, is an ideal system to look for such an exotic state in the form of antiferromagnetic Cu 2 + kagome planes. The x = 1 end member, named herbertsmithite, has shown promising spin liquid properties from prior studies on powder samples. Here we show a new synthesis by which high-quality centimeter-sized single crystals of Znparatacamite have been produced for the first time. Neutron and synchrotron xray diffraction experiments indicate no structural transition down to T = 2 K. The magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured for the x = 1 sample. A small, temperature-dependent anisotropy has been observed, where chi z / chip > 1 at high temperatures and chiz / chip < 1 at low temperatures. Fits of the high-temperature data to a Curie-Weiss model also reveal anisotropies for thetacw's and g-factors. By comparing with theoretical calculations, the presence of a small easy-axis exchange anisotropy can be deduced as a primary perturbation to the dominant Heisenberg nearest neighbor interaction. These results have great bearing on the interpretation of theoretical calculations based on the kagome Heisenberg antiferromagnet model to the experiments on ZnCu3(OH) 6Cl2. Specific heat measurements down to dilution temperatures and under strong applied magnetic fields show a superlinear temperature dependence with a finite linear term. Most importantly, we present neutron scattering measurements of the
Putz, Ana-Maria; Putz, Mihai V
2012-01-01
The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands' assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature.
Putz, Ana-Maria; Putz, Mihai V.
2012-01-01
The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature. PMID:23443102
Sensitivity of a cavityless opto-mechanical system
NASA Astrophysics Data System (ADS)
Fermani, Rachele; Mancini, Stefano; Tombesi, Paolo
2004-05-01
Optomechanical systems play a crucial role in a variety of precision measurement like gravitational wave detection and atomic force microscope. They are based on the interaction between a movable mirror, a meter experiencing tiny forces, and a radiation field, a probe reading out the mirror's position. In these applications one needs a very high resolution measurement and a good control of the various noise sources, classical and quantum, because one has to detect the effect of a very weak force. As optomechanical system, it is usually considered a Fabry-Perot cavity with a movable mirror coupled to the external force and to the radiation probe. Instead, in our work, we consider a single perfectly reflecting mirror shined by an intense and quasi-monochromatic optical beam. The physical process is very similar to a stimulate Brillouin scattering, even though in this case the Stokes and anti-Stokes component are back scattered by the acoustic wave at reflection, and the optomechanical coupling is provided by the radiation pressure. An effective interaction Hamiltonian for that system has been derived; we further consider the action of a classical coherent force on the probe and its readout through radiation field. Since the Hamiltonian was written in a frame rotating at the frequency of the mirror, we obtain a new Hamiltonian whit new related Heisenberg equations, by assuming the force constant. The mirror is considered initially in a thermal state, and the meter modes in pure entangled state (two mode squeezed state). Then, supposing to perform the heterodyne detection on the reflected sidebands modes, the relevant quantities for the sensitivity of the system are determined to get the signal to noise ratio, from which the minimum detectable force is also obtained. The latter is compared with the standard quantum limit (SQL), showing the possibility to go beyond it by using nonclassical entangled state, (likewise to what happens in the model involving an optical
Critical behavior of isotropic three-dimensional systems with dipole-dipole interactions
Belim, S. M.
2013-06-15
The critical behavior of Heisenberg magnets with dipole-dipole interactions near the line of second-order phase transitions directly in three-dimensional space is investigated in terms of a field-theoretic approach. The dependences of critical exponents on the dipole-dipole interaction parameter are derived. Comparison with experimental facts is made.
Versatile approach to spin dynamics in correlated electron systems
NASA Astrophysics Data System (ADS)
Behrmann, Malte; Lichtenstein, Alexander I.; Katsnelson, Mikhail I.; Lechermann, Frank
2016-10-01
Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner-Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However, many experimental studies, e.g., of (de)magnetization processes, focus on itinerant local-moment materials, such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows us to treat nonequilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.
NASA Astrophysics Data System (ADS)
Balázs, András
2016-01-01
The Heisenberg-James-Stapp (quantum mechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantum mechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantum mechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.
Florez, J M; Vargas, P; Garcia, C; Ross, C A
2013-06-01
Monte Carlo modeling suggests that the magnetothermal features of the Fe2P-structured FeCrAs-like compound offer a promising route for the design of magnetocaloric materials. The prototype structure is modeled as antiferromagnetically coupled layered Heisenberg systems mimicking the distorted Kagome/triangular stacked architecture of FeCrAs iron-pnictide. The magnetic entropy change ΔSm(T) presents a plateau-like behavior which can be tailored by tuning either the JCr-Fe/JCr-Cr exchange energy ratio or the magnetic field. The plateau is defined by cooperative spin ordering within a ferrimagnetic region which exists between two critical temperatures separating at the lower bound (Tac) a canted antiferromagnetic phase and at the upper bound (Tdc) the thermally disordered phase. The refrigerant capacity and adiabatic change of temperature are A(H)(Tdc - Tac) and A(H)Tp/Cm respectively, with Tac < Tp < Tdc, A(H) an increasing positive function of the field defining the height of the plateau and Cm the magnetic specific heat, whose critical behavior is related to the T(a,d)(c) values.
Solar system positioning system
NASA Technical Reports Server (NTRS)
Penanen, Konstantin I.; Chui, Talso
2006-01-01
Power-rich spacecraft envisioned in Prometheus initiative open up possibilities for long-range high-rate communication. A constellation of spacecraft on orbits several A.U. from the Sun, equipped with laser transponders and precise clocks can be configured to measure their mutual distances to within few cm. High on-board power can create substantial non-inertial contribution to the spacecraft trajectory. We propose to alleviate this contribution by employing secondary ranging to a passive daughter spacecraft. Such constellation can form the basis of it navigation system capable of providing position information anywhere in the soIar system with similar accuracy. Apart from obvious Solar System exploration implications, this system can provide robust reference for GPS and its successors.
Başar, Erol; Güntekin, Bahar
2007-04-01
metaphor of "finding the walking path in a cloudy or foggy day". This is meant by stating "The Nebulous Cartesian System" (NCS). Descartes, at his time undertaking his genius step, did not possess the knowledge of today's physiology and modern physics; we think that the time has come to consider such a New Cartesian System. To deal with this, we propose the utilization of the Heisenberg S-Matrix and a modified version of the Feynman Diagrams which we call "Brain Feynman Diagrams". Another metaphor to consider within the oscillatory approach of the NCS is the "string theory". We also emphasize that fundamental steps should be undertaken in order to create the own dynamical framework of the brain-body-mind incorporation; suggestions or metaphors from physics and mathematics are useful; however, the grammar of the brains intrinsic language must be understood with the help of a new biologically founded, adaptive-probabilistic Cartesian system. This new Cartesian System will undergo mutations and transcend to the philosophy of Henri Bergson in parallel to the Evolution theory of Charles Darwin to open gateways for approaching the brain-body-mind problem.
NASA Astrophysics Data System (ADS)
Atanasov, Atanas Todorov
2014-10-01
The scaling of physical and biological characteristics of the living organisms is a basic method for searching of new biophysical laws. In series of previous studies the author showed that in Poikilotherms, Mammals and Aves, the volume to surface ratio V×S-1 (m) of organisms is proportional to their generation time Tgt(s) via growth rate v (m s-1): V×S-1 = vgr×Tr. The power and the correlation coefficients are near to 1.0. Aim of this study is: i) to prove with experimental data the validity of the above equation for Unicellular organisms and ii) to show that perhaps, the cells are quantum-mechanical systems. The data for body mass M (kg), density ρ (kg/m3), minimum and maximum doubling time Tdt (s) for 50 unicellular organisms are assembled from scientific sources, and the computer program `Statistics' is used for calculations. In result i) the analytical relationship from type: V×S-1 = 4.46ṡ10-11×Tdt was found, where vgr = 4.46×10-11 m/s and ii) it is shown that the products between cell mass M, cell length expressed by V/S ratio and growth rate vgr satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M×vgr>h/2π and Tdt×M×vgr2>h/2π are valid, where h= 6.626×10-34 Jṡs is the Planck constant. This rise the question: do cells appear quantum-mechanical systems?
Atanasov, Atanas Todorov
2014-10-06
The scaling of physical and biological characteristics of the living organisms is a basic method for searching of new biophysical laws. In series of previous studies the author showed that in Poikilotherms, Mammals and Aves, the volume to surface ratio V×S{sup −1} (m) of organisms is proportional to their generation time T{sub gt}(s) via growth rate v (m s{sup −1}): V×S{sup −1} = v{sub gr}×T{sup r}. The power and the correlation coefficients are near to 1.0. Aim of this study is: i) to prove with experimental data the validity of the above equation for Unicellular organisms and ii) to show that perhaps, the cells are quantum-mechanical systems. The data for body mass M (kg), density ρ (kg/m{sup 3}), minimum and maximum doubling time T{sub dt} (s) for 50 unicellular organisms are assembled from scientific sources, and the computer program ‘Statistics’ is used for calculations. In result i) the analytical relationship from type: V×S{sup −1} = 4.46⋅10{sup −11}×T{sub dt} was found, where v{sub gr} = 4.46×10{sup −11} m/s and ii) it is shown that the products between cell mass M, cell length expressed by V/S ratio and growth rate v{sub gr} satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M×v{sub gr}>h/2π and T{sub dt}×M×v{sub gr}{sup 2}>h/2π are valid, where h= 6.626×10{sup −34} J⋅s is the Planck constant. This rise the question: do cells appear quantum-mechanical systems?.
... How Can I Help a Friend Who Cuts? Immune System KidsHealth > For Teens > Immune System Print A A ... could put us out of commission. What the Immune System Does The immune (pronounced: ih-MYOON) system, which ...
In the name of science: don't tamper with the deceptive truth...
Reis, Helton J; Mukhamedyarov, Marat A; Rizvanov, Albert A; Palotás, András
2009-12-01
Werner Heisenberg (1901-1976) is one of the most controversial, most ambivalent and most important figures in the history of modern science. The debate surrounding him with respect to nuclear weapons and National Socialism appears unending. Even though Heisenberg's uncertainty principle of the quantum system and his involvement in the Nazi atomic bomb project have been thoroughly discussed in various journals over the past decades, no communication has ever been published at a holistic level of his greatest Nobel-prize winning achievement in theoretical physics. In order to fill up this hole, this piece explicitly communicates the Heisenberg's paradox at all levels of science.
In the name of science: don't tamper with the deceptive truth...
Reis, Helton J; Mukhamedyarov, Marat A; Rizvanov, Albert A; Palotás, András
2009-12-01
Werner Heisenberg (1901-1976) is one of the most controversial, most ambivalent and most important figures in the history of modern science. The debate surrounding him with respect to nuclear weapons and National Socialism appears unending. Even though Heisenberg's uncertainty principle of the quantum system and his involvement in the Nazi atomic bomb project have been thoroughly discussed in various journals over the past decades, no communication has ever been published at a holistic level of his greatest Nobel-prize winning achievement in theoretical physics. In order to fill up this hole, this piece explicitly communicates the Heisenberg's paradox at all levels of science. PMID:20105124
NASA Astrophysics Data System (ADS)
Moortgat-Pick, Gudrid
2009-12-01
A short summary is given on the key points of the Furry picture. It describes quantum mechanical systems in external fields. It differs therefore from the quantum mechanical Schrödinger, Heisenberg and interaction representations.
Dwyer, Sheila
2014-11-01
You can’t beat the Heisenberg uncertainty principle, but you can engineer systems so that most of the uncertainty is in the variable of your choice. Doing so can improve the precision of delicate measurements.
ERIC Educational Resources Information Center
Denning, Peter J.; Brown, Robert L.
1984-01-01
A computer operating system spans multiple layers of complexity, from commands entered at a keyboard to the details of electronic switching. In addition, the system is organized as a hierarchy of abstractions. Various parts of such a system and system dynamics (using the Unix operating system as an example) are described. (JN)
Non uniqueness and equivalence of the q-deformed Weyl-Heisenberg algebra representations
NASA Astrophysics Data System (ADS)
Boucerredj, N.; Mebarki, N.
2012-06-01
The non uniqueness and equivalence of the q-deformed Weyl-Heinsenberg algebra are studied in the weak deformation parameter approximation. It turns out that the Macfarlane representation is not unique leading to inequivalant solutions of the q-deformed coherent states. Moreover, it is shown that the Krolikowski representation gives also a completely different result for the same algebra.
NASA Astrophysics Data System (ADS)
Latimer, D. C.
2007-06-01
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase-space of the two-dimensional isotropic harmonic oscillator. Using Dirac’s quantization condition, the authors investigate how these alternative symplectic forms affect this system’s quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent.
Heisenberg spin bus as a robust transmission line for quantum-state transfer
Oh, Sangchul; Hu Xuedong; Wu Lianao; Shim, Yun-Pil; Fei, Jianjia; Friesen, Mark
2011-08-15
We study quantum-state transfer (QST) through a strongly coupled antiferromagnetic spin chain (acting as a spin bus), between weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that QST is enabled specifically by the second-order terms in the perturbative expansion. We show that QST is robust against disorder in the couplings, either within the bus or to the external qubits. We find that the protocol works when the qubits are attached to any node on an even-size bus or to the antiferromagnetic nodes on an odd-size bus. The optimal time for QST is found to depend nonmonotonically on qubit separation.
Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
NASA Astrophysics Data System (ADS)
Miyadera, Takayuki; Imai, Hideki
2008-11-01
A limitation on simultaneous measurement of two arbitrary positive-operator-valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner’s formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive-operator-valued measures to be simultaneously measurable is obtained.
Heisenberg magnetic chain with single-ion easy-plane anisotropy: Hubbard operators approach
NASA Astrophysics Data System (ADS)
Spirin, D. V.; Fridman, Yu. A.
2003-03-01
We investigate the gap in excitation spectrum of one-dimensional S=1 ferro- and antiferromagnets with easy-plane single-ion anisotropy. The self-consistent modification of Hubbard operators approach which enables to account single-site term exactly is used. For antiferromagnetic model we found Haldane phase that exists up to point D=4 J (where D is anisotropy parameter, J is exchange coupling), while quadrupolar phase realizes at larger values of anisotropy. Our results specify those of Golinelli et al. (Phys. Rev. B. 45 (1992) 9798), where similar model was studied. Besides the method gives gap value closer to numerical estimations than usual spin-wave theories.
Remarks towards the spectrum of the Heisenberg spin chain type models
NASA Astrophysics Data System (ADS)
Burdík, Č.; Fuksa, J.; Isaev, A. P.; Krivonos, S. O.; Navrátil, O.
2015-05-01
The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is considered. Finally, we discuss some questions relating to the general open Hecke chain models.
Bornstein, Robert F
2009-01-01
During the past 100 years, advances in personality assessment have paralleled key events in art and physics; but for the most part, these parallels have gone unrecognized. In this article, I discuss the ways in which 2 movements in 20th-century art (cubism and nonrepresentational painting) and 2 principles from 20th-century physics (the uncertainty principle and the observer effect) combined to create an intellectual context for the process dissociation approach to personality assessment, a research strategy wherein naturally occurring influences on test scores are deliberately manipulated to illuminate underlying response processes. I discuss core elements of a process-focused paradigm for 21st-century personality assessment including (a) the need for researchers to explore test score divergences as well as convergences, (b) a view of the assessor as active shaper (rather than dispassionate observer) of testee behavior, and (c) the importance of integrating personality assessment concepts and methods with ideas and findings from disciplines within and outside psychology. PMID:19085275