NASA Astrophysics Data System (ADS)
Sun, Fadi; Ye, Jinwu; Liu, Wu-Ming
2015-03-01
We show that Rotated Heisenberg (RH) model is a new class of quantum spin models to describe magnetic materials with strong spin-orbit couplings (SOC). We introduce Wilson loops to characterize frustrations and gauge equivalent class. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground state. It supports a novel gapped elementary excitation named as in-commensurate magnons which have two gap minima continuously tuned by the SOC strength. At low temperatures, the in-commensurate magnons lead to dramatic effects in all physical quantities such as density of states, specific heat, magnetization and various spin correlation functions. At high temperatures, the specific heat and transverse spin structure factors depend on the SOC strength explicitly. We argue that one gauge may be realized in current experiments and other gauges may also be realized in near future experiments. Various experimental detections are discussed. This work is supported by NSF-DMR-1161497, NSFC-11174210.
NASA Astrophysics Data System (ADS)
Ghorbani, Elaheh; Tocchio, Luca F.; Becca, Federico
2016-02-01
By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have superexchange couplings J and the third one has instead J'. This model interpolates between the square lattice and the isotropic triangular one, for J'/J ≤1 , and between the isotropic triangular lattice and a set of decoupled chains, for J /J'≤1 . We consider all the fully symmetric spin liquids that can be constructed with the fermionic projective-symmetry group classification (Zhou and Wen, arXiv:cond-mat/0210662) and we compare them with the spiral magnetic orders that can be accommodated on finite clusters. Our results show that, for J'/J ≤1 , the phase diagram is dominated by magnetic orderings, even though a spin-liquid state may be possible in a small parameter window, i.e., 0.7 ≲J'/J ≲0.8 . In contrast, for J /J'≤1 , a large spin-liquid region appears close to the limit of decoupled chains, i.e., for J /J'≲0.6 , while magnetically ordered phases with spiral order are stabilized close to the isotropic point.
Monte Carlo Simulations of inter- and intra-grain spin structure of Ising and Heisenberg models
NASA Astrophysics Data System (ADS)
Leblanc, Martin
In order to keep supplying computer hard disk drives with more and more storage space, it is essential to have smaller bits. With smaller bits, superparamagnetism, the spontaneous flipping of the magnetic moments in a bit caused by thermal fluctuations, becomes increasingly important and impacts the stability of stored data. Recording media is composed of magnetic grains (usually made of CoCrPt alloys) roughly 10 nm in size from which bits are composed. Most modeling efforts that study magnetic recording media treat the grains as weakly interacting uniformly magnetized objects. In this work, the spin structure internal to a grain is examined along with the impact of varying the relative strengths of intrar-grain and inter-grain exchange interactions. The interplay between these two effects needs to be examined for a greater understanding of superparamagnetism as well as for the applications of the proposed Heat Assisted Magnetic Recording (HAMR) technology where thermal fluctuations facilitate head-field induced bit reversal in high anisotropy media. Simulations using the Monte Carlo method (with cluster-flipping algorithms) are performed on a 2D single-layer and multilayer Ising model with a strong intrar-grain exchange interaction J as well as a weak inter-grain exchange J'. A strong deviation from traditional behavior is found when J'/J is significant. M-H hysteresis loops are also calculated and the coercivity, H c is estimated. A large value represents a strong resilience to the superparamagnetic effect. It is found that taking into account the internal degrees of freedom has a significant effect on Hce. As the Ising model serves only as an approximation, preliminary simulations are also reported on a more realistic Heisenberg model with uniaxial anisotropy. Key Words: Ising model, Heisenberg model, Monte Carlo Simulation
EDITORIAL: J J Thomson's Electron
NASA Astrophysics Data System (ADS)
Adams, Steve
1997-07-01
Westminster School, London, UK A few weeks ago David Thomson, J J Thomson's grandson, presented a Friday evening discourse at the Royal Institution. In it he traced the development of JJT's life from his early studies at Owen's College in Manchester, on to Trinity College Cambridge, his work under Rayleigh at the Cavendish, and his succession as Professor of Experimental Physics in 1884 (a post he passed on to Rutherford in 1919). These were years of heroic discoveries that shaped 20th century physics. Looking around the lecture theatre at all the bow-ties and dinner jackets, it must have been rather similar on 30 April 1897 when JJT delivered his famous discourse on 'Cathode Rays' in which he cautiously but confidently announced that his own results together with those of other experimenters (Lenard in particular):
`....seem to favour the hypothesis that the carriers of the charges are smaller than the atoms of hydrogen.'In this issue articles by Leif Gerward and Christopher Cousins, and by Isobel Falconer explore the historical and philosophical context of that discovery. The sound-bites to history in many A-level courses have JJT as both the hero who single-handedly discovered the electron and the rather naive Victorian scientist who thought the atom was a plum pudding. It is valuable to see how Thomson's work pulled the threads of many experiments together and to realize that he may have been first to the post because of a difference in the philosophical approach to cathode rays in Britain compared to Europe. Experimental data must always be interpreted, and divergent philosophies can lead to quite different conclusions. The electron was, of course, the first subatomic particle to be identified. Christine Sutton's article looks at how 20th century discoveries reveal Nature's mysterious habit of repeating successful patterns---electrons for example have very close relations, the muon and the tau---but why? Perhaps the answer will come
Thermal entanglement in a four-qubit Heisenberg spin model with external magnetic fields
NASA Astrophysics Data System (ADS)
Wu, Ke-Dong; Zhou, Bin; Cao, Wan-Qiang
2007-03-01
The entanglement properties both in the four-qubit anisotropic Heisenberg XY chain with uniform external magnetic fields and in the Heisenberg XX model with two external fields are investigated. The analytical expressions for the measures of entanglement are obtained. In Heisenberg XY chain, the effects of the anisotropy on the thermal entanglement are studied. In the Heisenberg XX ring with two external fields, it is found that a high pair entanglement can be obtained.
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.
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.
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.
A Symmetrized Basis for Transitions in the Heisenberg Model
NASA Astrophysics Data System (ADS)
Haydock, Roger; Nex, C. M. M.
2013-03-01
The spin-S Heisenberg model has 2S+1 states on each site, for which there are (2S+1)2 possible transitions between these states. For N sites there are (2S+1)N states and (2S+1)2N transitions between states. This rapid increase in the number of transitions with sites appears to limit calculations to just a few sites. However for transitions induced by spin-spin interactions, we construct a symmetrized basis which only grows as 2N-3, making possible computations for much larger systems. Supported by the Richmond F. Snyder Fund.
Chiral Spin Liquid in a Frustrated Anisotropic Kagome Heisenberg Model
NASA Astrophysics Data System (ADS)
He, Yin-Chen; Sheng, D. N.; Chen, Yan
2014-04-01
Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor—anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.
Spin Liquid in the Triangular Lattice Heisenberg Model
NASA Astrophysics Data System (ADS)
McCulloch, Ian; Saadatmand, Seyed
We report the results of a large-scale numerical study of the spin-1/2 Heisenberg model on the triangular lattice, with nearest- and next-nearest neighbor interactions. Using SU(2)-invariant iDMRG for infinite cylinders, we focus on the YC12 structure (with a circumference of 12 sites), and obtain 4 candidate groundstates, corresponding to even/odd spinon sectors, each with linear and projective representations of the cylinder geometry. The momentum-resolved entanglement spectrum reveals the structure of the low-lying spinon excitations. Contrary to some recent works, we find no evidence for chiral symmetry breaking. Supported by the ARC Centre for Engineered Quantum Systems.
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.
Landau-Heisenberg Hamiltonian model for FeRh
NASA Astrophysics Data System (ADS)
Derlet, P. M.
2012-05-01
An empirical model is developed for the FeRh system with the view of gaining further insight into the first-order antiferromagnetic-ferromagnetic (AFM-FM) and volume phase transition known to occur at 370 K. A volume-per-atom dependent minimal nearest neighbor Landau-Heisenberg Hamiltonian is employed in which longitudinal and transverse moment fluctuations are considered for both the Fe and Rh atoms. As a function of volume-per-atom, the corresponding onsite Landau function coefficients and the nearest-neighbor exchange parameters are fitted directly to a wide range of existing colinear and noncolinear density functional theory calculations. Using a developed Monte Carlo strategy the thermal properties of the AFM and FM phases are investigated, as well as the phase transition. It is found that the model is able to describe well the thermal expansion, heat capacities and the associated entropy increase that accompanies the magnetic/volume phase transition. The model suggests an equally important role for the magnetic and volume fluctuations in driving the phase transition.
Frustrated square lattice Heisenberg model and magnetism in Iron Telluride
NASA Astrophysics Data System (ADS)
Zaliznyak, Igor; Xu, Zhijun; Gu, Genda; Tranquada, John; Stone, Matthew
2011-03-01
We have measured spin excitations in iron telluride Fe1.1Te, the parent material of (1,1) family of iron-based superconductors. It has been recognized that J1-J2-J3 frustrated Heisenberg model on a square lattice might be relevant for the unusual magnetism and, perhaps, the superconductivity in cuprates [1,2]. Recent neutron scattering measurements show that similar frustrated model might also provide reasonable account for magnetic excitations in iron pnictide materials. We find that it also describes general features of spin excitations in FeTe parent compound observed in our recent neutron measurements, as well as in those by other groups. Results imply proximity of magnetic system to the limit of extreme frustration. Selection of spin ground state under such conditions could be driven by weak extrinsic interactions, such as lattice distortion, or strain. Consequently, different nonuniversal types of magnetic order could arise, both commensurate and incommensurate. These are not necessarily intrinsic to an ideal J1-J2-J3 model, but might result from lifting of its near degeneracy by weak extrinsic perturbations.
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.
J. J. Thomson goes to America.
Downard, Kevin M
2009-11-01
Joseph John (J. J.) Thomson was an accomplished scientist who helped lay the foundations of nuclear physics. A humble man of working class roots, Thomson went on to become one of the most influential physicists of the late 19th century. He is credited with the discovery of the electron, received a Nobel Prize in physics in 1906 for investigations into the conduction of electricity by gases, was knighted in 1908, and served as a Cavendish Professor and Director of the laboratory for over 35 years from 1884. His laboratory attracted some of the world's brightest minds; Francis W. Aston, Niels H. D. Bohr, Hugh L. Callendar, Charles T. R. Wilson, Ernest Rutherford, George F. C. Searle, Geoffrey I. Taylor, and John S. E. Townsend all worked under him. This article recounts J. J. Thomson's visits to North America in 1896, 1903, 1909, and finally 1923. It presents his activities and his personal impressions of the people and society of the U.S.A. and Canada, and the science of atomic physics and chemistry in the late 1800s and early 1900s. PMID:19734055
The infinite range Heisenberg model and high temperature superconductivity
NASA Astrophysics Data System (ADS)
Tahir-Kheli, Jamil
1992-01-01
The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models.Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes.Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts.Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.
Infinite-range Heisenberg model and high-temperature superconductivity
NASA Astrophysics Data System (ADS)
Tahir-Kheli, Jamil; Goddard, William A., III
1993-11-01
A strongly coupled variational wave function, the doublet spin-projected Néel state (DSPN), is proposed for oxygen holes in three-band models of high-temperature superconductors. This wave function has the three-spin system of the oxygen hole plus the two neighboring copper atoms coupled in a spin-1/2 doublet. The copper spins in the neighborhood of a hole are in an eigenstate of the infinite-range Heisenberg antiferromagnet (SPN state). The doublet three-spin magnetic polaron or hopping polaron (HP) is stabilized by the hopping terms tσ and tτ, rather than by the copper-oxygen antiferromagnetic coupling Jpd. Although, the HP has a large projection onto the Emery (Dg) polaron, a non-negligible amount of doublet-u (Du) character is required for optimal hopping stabilization. This is due to Jdd, the copper-copper antiferromagnetic coupling. For the copper spins near an oxygen hole, the copper-copper antiferromagnetic coupling can be considered to be almost infinite ranged, since the copper-spin-correlation length in the superconducting phase (0.06-0.25 holes per in-plane copper) is approximately equal to the mean separation of the holes (between 2 and 4 lattice spacings). The general DSPN wave function is constructed for the motion of a single quasiparticle in an antiferromagnetic background. The SPN state allows simple calculations of various couplings of the oxygen hole with the copper spins. The energy minimum is found at symmetry (π/2,π/2) and the bandwidth scales with Jdd. These results are in agreement with exact computations on a lattice. The coupling of the quasiparticles leads to an attraction of holes and its magnitude is estimated.
Burgos, José E; Donahoe, John W
2016-05-01
An article published in Behavioural Processes (Calvin and McDowell, 2015) contemplated that the approach to neural networks developed by the present authors cannot simulate certain behavioral findings, notably the Kamin blocking effect and successive conditioning. Here we demonstrate that these concerns are unwarranted as an overall characterization of the approach. In addition, several other more general issues identified in the target article are addressed as well. These include the determination of network architectures, the assignment-of-credit problem, the potential for catastrophic interference, and the falsifiability of the model. PMID:26970023
The J1-J2 Heisenberg model on the triangular lattice
NASA Astrophysics Data System (ADS)
McCulloch, Ian; Saadatmand, Seyed; Powell, Ben
2015-03-01
We study the J1-J2 spin-1/2 Heisenberg model on triangular cylinders using non-abelian DMRG techniques. This model exhibits a rich phase diagram in the J1-J2 plane with a quasi-long-range 120° order, valence-bond crystal and columnar phases. ARC Centre for Engineered Quantum Systems.
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
NASA Astrophysics Data System (ADS)
Yao, Xiaoyan; Dong, Shuai
2016-05-01
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.
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)
Farnell, D. J. J.; Darradi, R.; Schmidt, R.; Richter, J.
2011-09-01
We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized J-J' model interpolating between both systems by varying J'/J from J'/J=0 (bounce limit) to J'/J=1 (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the “pure” bounce (J'/J=0) and maple-leaf (J'/J=1) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range 0⩽J'/J≲Jc'/J and that the magnetic order parameter varies only weakly with J'/J. At Jc'≈1.45J, a transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place that is probably of first-order type, although we cannot rule out that this transition is second order. The orthogonal-dimer state is the exact ground state in this large-J' regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We find a 1/3 magnetization plateau for J'/J≳1.07 and another one at 2/3 of saturation emerging only at large J'/J≳3.
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.
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.
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.
Second-order Peierls transition in the spin-orbital Kumar-Heisenberg model
NASA Astrophysics Data System (ADS)
Brzezicki, Wojciech; Hagymási, Imre; Dziarmaga, Jacek; Legeza, Örs
2015-05-01
We add a Heisenberg interaction term ∝λ in the one-dimensional SU(2 )⊗XY spin-orbital model introduced by Kumar. At λ =0 the spin and orbital degrees of freedom can be separated by a unitary transformation leading to an exact solution of the model. We show that a finite λ >0 leads to spontaneous dimerization of the system which in the thermodynamic limit becomes a smooth phase transition at λ →0 , whereas it remains discontinuous within the first-order perturbation approach. We present the behavior of the entanglement entropy, energy gap, and dimerization order parameter in the limit of λ →0 confirming the critical behavior. Finally, we show the evidence of another phase transition in the Heisenberg limit, λ →∞ , and give a qualitative analytical explanation of the observed dimerized states both in the limit of small and large λ .
Role of Topological Defects in the Phase Transition of the Three-Dimensional Heisenberg Model.
NASA Astrophysics Data System (ADS)
Lau, Manhot
The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a 'chemical potential' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to paramagnetic phase to occur. Such a conclusion is also consistent with a Renormalization Group study of the O(n) model, which suggests that topological defects should be explicitly taken into account for a correct description of the critical behavior in models including the three-dimensional Heisenberg model.
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.
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.
Magnetic order and spin excitations in the Kitaev-Heisenberg model on a honeycomb lattice
NASA Astrophysics Data System (ADS)
Vladimirov, A. A.; Ihle, D.; Plakida, N. M.
2016-06-01
We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev-Heisenberg model proposed for A2IrO3 (A = Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation for four different ordered phases observed in the parameter space of the model: antiferromagnetic, stripe, ferromagnetic, and zigzag phases. The Néel temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na2IrO3.
Cathode Ray Research Leading to J.J. Thomson's Discovery
NASA Astrophysics Data System (ADS)
Mulligan, Joseph
1997-04-01
This paper reviews the research on the properties and nature of cathode rays that led to the discovery of the electron by J. J. Thomson in the years 1897 - 1899. During the period from about 1870 to 1897 important research on cathode rays was carried out by William Crookes and Arthur Schuster in England, by Eugen Goldstein, Heinrich Hertz, Philipp Lenard, Emil Wiechert and Walter Kaufman in Germany, and by Jean Perrin in France. This research was always tedious and often inexact because fast vacuum pumps and convenient vacuum gauges did not yet exist. Still a few of these earlier researchers narrowly missed beating J. J. Thomson to the discover of the electron.
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.
Interplay of localized and itinerant behavior in the one-dimensional Kondo-Heisenberg model
NASA Astrophysics Data System (ADS)
Xie, Neng; Yang, Yi-feng
2015-05-01
We use the density matrix renormalization group method to study the interplay of the localized and itinerant behaviors in the one-dimensional Kondo-Heisenberg model. We find signatures of simultaneously localized and itinerant behaviors of the local spins and attribute this duality to their simultaneous entanglement within the spin chain and with conduction electrons due to incomplete hybridization. We propose a microscopic definition of the hybridization parameter that measures this "partial" itinerancy. Our results provide a microscopic support for the dual nature of f electrons and the resulting two-fluid behavior widely observed in heavy electron materials.
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.
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.
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.
Density-matrix renormalization group study of the extended Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Shinjo, Kazuya; Sota, Shigetoshi; Tohyama, Takami
2015-02-01
We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a 120∘ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.
The Quantum Refrigerator in a Two-Qubit Xxz Heisenberg Model
NASA Astrophysics Data System (ADS)
Albayrak, Erhan
2013-05-01
The four-level entangled quantum refrigerator (QR) is studied in the XXZ Heisenberg model for the two-qubits. The Hamiltonian of the problem includes the exchange parameters Jx = Jy = J and Jz = αJ along the x-, y- and z-directions, respectively, and constant external magnetic field B in the z-direction. The parameter α is introduced into the model which controls the strength of the exchange parameter Jz in comparison to Jx and Jy, thus, our investigation of QR includes the XX (α = 0.0), XXX (α = 1.0) and XXZ (for other α's) Heisenberg models. The two-qubits are assumed to be in contact with two heat reservoirs at different temperatures. The concurrences for a two-qubit are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency are derived. The contour, i.e., the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are illustrated.
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.
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
Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
NASA Astrophysics Data System (ADS)
Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.
2014-09-01
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.
NASA Astrophysics Data System (ADS)
Parente, Walter E. F.; Pacobahyba, J. T. M.; Araújo, Ijanílio G.; Neto, Minos A.; Ricardo de Sousa, J.
2015-11-01
We will study phase diagram the quantum spin-1/2 anisotropic Heisenberg antiferromagnet model in the presence of a Dzyaloshinskii-Moriya interaction (D) and a uniform longitudinal (H) magnetic field, where we have observed an anomaly at low temperatures. Using the effective-field theory with a finite cluster N=2 spin (EFT-2) we calculate the phase diagram in the H - D plane on a simple cubic lattice (z=6). We analyzed the cases: anisotropic Heisenberg - case I: (Δ = 1), anisotropic Heisenberg - case II: (Δ = 0.5) and anisotropic Heisenberg - case III: (Δ = 0), where only second order phase transitions are observed.
Girardeau, M. D.
2006-11-24
The ground and excited states of a one-dimensional (1D) spin-(1/2) Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.
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.
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.
Thermal entanglement in the Heisenberg XXZ model with Dzyaloshinskii-Moriya interaction
NASA Astrophysics Data System (ADS)
Li, Sha-Sha; Ren, Ting-Qi; Kong, Xiang-Mu; Liu, Kai
2012-01-01
By the concept of negativity, we investigate the thermal entanglement in the two-spin (1/2 >,s) Heisenberg XXX and XXZ models in the presence of Dzyaloshinskii-Moriya (DM) interactions respectively. Through calculation, we know that for the XXZ model, the Δ and s can be used together to control the extent of entanglement and, in particular, to obtain large entanglement. The effect of spin in both models shows that it can increase the critical temperature and the negativity decreases as the spin increases. We found that the DM interaction has different effects on Fermi and Bose systems so it can not only excite entanglement but also affect the entanglement in different spin systems.
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.
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:
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.
NASA Astrophysics Data System (ADS)
Pasrija, Kanika; Kumar, Sanjeev
2016-05-01
We present a Monte Carlo simulation study of a bilinear-biquadratic Heisenberg model on a two-dimensional square lattice in the presence of an external magnetic field. The study is motivated by the relevance of this simple model to the non-collinear magnetism and the consequent ferroelectric behavior in the recently discovered high-temperature multiferroic, cupric oxide (CuO). We show that an external magnetic field stabilizes a non-coplanar magnetic phase, which is characterized by a finite ferromagnetic moment along the direction of the applied magnetic field and a spiral spin texture if projected in the plane perpendicular to the magnetic field. Real-space analysis highlights a coexistence of non-collinear regions with ferromagnetic clusters. The results are also supported by simple variational calculations.
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.
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.
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.
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 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
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.
Effect of the site dilution on spin transport in the two-dimensional biquadratic Heisenberg model
NASA Astrophysics Data System (ADS)
Lima, L. S.
2016-05-01
We use the SU(3) Schwinger's boson theory to study the spin transport in the biquadratic Heisenberg chains in a square lattice with a distribution of non-magnetic impurities on the lattice. We verify the influence of the site dilution in the Ac and Dc spin conductivities of this model in the Bose-Einstein condensation regime in which the bosons t are condensed. Our results show that the decreasing of the gap Δ with -β suffers a change for different concentrations x of non-magnetic impurities, however the point (in the -β axis) where the gap cancels does not change with x. Therefore, the size of the region ω, where the spin conductivity goes to zero decreases with the increase of x until the point where x=0.5, where the size of this region tends to zero.
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
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
Events Leading to J. J. Thomson's Electron in 1897
NASA Astrophysics Data System (ADS)
Dahl, Per F.
1997-03-01
The electron had its genesis in the glow discharge studies of the German school of Julius Plucker and company, who viewed their Kathodenstrahlen as a form of aetheral wave propagation. Next on the scene came the Victorian amateur scientists, personified by the incomparable William Crookes, who interpreted the rays in terms of material particulate behavior. Back on the Continent, meanwhile, there was Heinrich Hertz and his disciple Philipp Lenard--the latter with his metallic ``window'' and all it stood for. In England, an experimental rivalry ensued between J. J. Thomson and Arthur Schuster, who nearly beat ``J.J.'' to his corpuscle in 1890, while in Paris, about then, Jean Perrin's cathode ray studies were provoked by the lingering anti-atomic stance of his academic countrymen. The chronicle culminated in the charge-to-mass experiments of 1896-97, in which Emil Wiechert and Walter Kaufmann narrowly missed the electron in favor of Thomson and his classic e/m determinations.
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
NASA Astrophysics Data System (ADS)
Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan
2012-06-01
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 hc = 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.
The phase transition in the anisotropic Heisenberg model with long range dipolar interactions
NASA Astrophysics Data System (ADS)
Mól, L. A. S.; Costa, B. V.
2014-03-01
In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagree with the Renormalization Group results of Maier and Schwabl [Phys. Rev. B, 70, 134430 (2004)] [13] and the results of Rapini et al. [Phys. Rev. B, 75, 014425 (2007)] [12], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results show that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.
NASA Astrophysics Data System (ADS)
Yang, Li-Jun; Cao, Jun-Peng; Yang, Wen-Li
2015-10-01
We propose an integrable spin-1/2 Heisenberg model where the exchange couplings and Dzyloshinky-Moriya interactions are dependent on the sites. By employing the quantum inverse scattering method, we obtain the eigenvalues and the Bethe ansatz equation of the system with the periodic boundary condition. Furthermore, we obtain the exact solution and study the boundary effect of the system with the anti-periodic boundary condition via the off-diagonal Bethe ansatz. The operator identities of the transfer matrix at the inhomogeneous points are proved at the operator level. We construct the T-Q relation based on them. From which, we obtain the energy spectrum of the system. The corresponding eigenstates are also constructed. We find an interesting coherence state that is induced by the topological boundary. Project supported by the National Natural Science Foundation of China (Grant Nos. 11174335, 11375141, 11374334, and 11434013) and the National Program for Basic Research of China and the Fund from the Chinese Academy of Sciences.
Obtaining model parameters for real materials from ab-initio calculations: Heisenberg exchange
NASA Astrophysics Data System (ADS)
Korotin, Dmitry; Mazurenko, Vladimir; Anisimov, Vladimir; Streltsov, Sergey
An approach to compute exchange parameters of the Heisenberg model in plane-wave based methods is presented. This calculation scheme is based on the Green's function method and Wannier function projection technique. It was implemented in the framework of the pseudopotential method and tested on such materials as NiO, FeO, Li2MnO3, and KCuF3. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and KCuF3. In the case of FeO our calculations explain the pressure dependence of the Néel temperature. Li2MnO3 turns out to be a Slater insulator with antiferromagnetic nearest neighbor exchange defined by the spin splitting. The proposed approach provides a unique way to analyze magnetic interactions, since it allows one to calculate orbital contributions to the total exchange coupling and study the mechanism of the exchange coupling. The work was supported by a grant from the Russian Scientific Foundation (Project No. 14-22-00004).
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).
NASA Astrophysics Data System (ADS)
Azzouz, M.; Asante, K. A.
2005-09-01
The antiferromagnetic Heisenberg model on the three-leg ladder is studied using the generalized Jordan-Wigner transformation in dimensions higher than 1, and the bond-mean-field theory. The magnetic susceptibility and other thermodynamic quantities are analyzed as a function of the rung-to-leg coupling ratio α and temperature T . We fit the experimental susceptibility data of the three-leg material Sr2Cu3O5 of Azuma and co-workers with good agreement. One of the main findings of this work is the proposal that close to two-thirds of the spin degrees of freedom on each of the rungs of the ladder lock at low T for small α , then collectively almost 2/3 of the spin degrees of freedom on all the rungs freeze completely at low T for α greater than a threshold value. The approach developed here can be used to study the three-leg ladder for all values of α , and is thus suitable for the description of the crossover regime between the weak- and strong-coupling regimes.
Z2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Daghofer, Maria; Rousochatzakis, Ioannis; Roessler, Ulrich K.; van den Brink, Jeroen
2013-03-01
Investigating the classical Kitaev-Heisenberg Hamiltonian on a triangular lattice, we establish the presence of an incommensurate non-coplanar magnetic phase, which is identified as a lattice of Z2 vortices. The vortices, topological point defects in the SO(3) order parameter of the nearby Heisenberg antiferromagnet, are not thermally excited but due to the spin-orbit coupling and arise at temperature T --> 0 . This Z2-vortex lattice is stable in a parameter regime relevant to iridates. We show that in the other, strongly anisotropic, limit a robust nematic phase emerges. Sponsored by the DFG (Emmy-Noether program).
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.
Existence of Néel Order in the S=1 Bilinear-Biquadratic Heisenberg Model via Random Loops
NASA Astrophysics Data System (ADS)
Lees, Benjamin
2016-05-01
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.
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.
Bichromatic magneto-optical trapping for J →J ,J -1 configurations
NASA Astrophysics Data System (ADS)
Cournol, Anne; Pillet, Pierre; Lignier, Hans; Comparat, Daniel
2016-05-01
A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for J →J ,J -1 transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the J →J -1 case (i.e., J''=1 →J'=0 ) and J →J case (i.e., J''=1 /2 →J'=1 /2 ). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the C2- molecular anion as a typical example of the interplay between the two simple transitions J →J ,J -1 .
Impurity entanglement in the J-J2-δ quantum spin chain
NASA Astrophysics Data System (ADS)
Deschner, Andreas; Sørensen, Erik S.
2011-10-01
The contribution to the entanglement of an impurity attached to one end of a J-J2-δ quantum spin chain (S = 1/2) is studied. Two different measures of the impurity contribution to the entanglement have been proposed: the impurity entanglement entropy Simp and the negativity {N} . The first, Simp, is based on a subtractive procedure where the entanglement entropy in the absence of the impurity is subtracted from results with the impurity present. The other, {N} , is the negativity of a part of the system separated from the impurity and the impurity itself. In this paper we compare the two measures and discuss their similarities and the differences between them. In the J-J2-δ model it is possible to perform very precise variational calculations close to the Majumdar-Ghosh point (J2 = J/2 and δ = 0) where the system is gapped with a dimerized ground state. We describe in detail how such calculations are done and how they can be used to calculate {N} as well as Simp for any impurity coupling JK. We then study the complete crossover in the impurity entanglement as JK is varied between 0 and 1 close to the Majumdar-Ghosh point. In particular, we study the impurity entanglement when a staggered nearest neighbour interaction proportional to δ is introduced. In this case we observe a very rapid reduction in the impurity entanglement as δ is increased.
Coherent States and Schwinger Models for Pseudo Generalization of the Heisenberg Algebra
NASA Astrophysics Data System (ADS)
Fakhri, H.; Mojaveri, B.; Dehghani, A.
We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with {PT} and {C} symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are {T}-pseudo-Hermiticity and {P}-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.
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
Entanglement in Mixed-Spin (1/2, 3/2) Heisenberg XXZ Model with Dzyaloshinskii-Moriya Interaction
NASA Astrophysics Data System (ADS)
Zhou, Chao-Biao; Xiao, Shu-Yuan; Zhang, Shao-Wu; Ran, Yang-Qiang
2016-02-01
In this paper, the entanglement in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous external magnetic field is studied. We not only calculate the ground-state entanglement but also investigate the behaviors of quantum phase transition following the changes of DM interaction and nonuniform magnetic field. More importantly, we note that the DM interaction improves the critical magnetic field B c , the critical temperature T c and broadens the region of entanglement.
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.
Comments on ""Lake Woebegone," Twenty Years Later" by J. J. Cannell, MD
ERIC Educational Resources Information Center
McRae, D. J.
2006-01-01
This article presents the author's comments on ""Lake Woebegone," Twenty Years Later" by J. J. Cannell, MD. J. J. Cannell's article on the so-called "Lake Woebegone" effect for K-12 educational testing systems is mostly an historical account of technical issues and policy considerations that led in part to development of new types of test…
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.
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
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.
NASA Astrophysics Data System (ADS)
Accioly, Antonio; Gaete, Patricio; Helaÿel-Neto, José A.
We calculate the lowest-order corrections to the static potential for both the generalized Born-Infeld electrodynamics and an Euler-Heisenberg-like model, in the presence of a constant external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a long-range correction ((1)/(r5)-type) to the Coulomb potential for the generalized Born-Infeld electrodynamics. Interestingly enough, in the Euler-Heisenberg-like model, the static potential remains Coulombian. Therefore, contrary to popular belief, the quantized truncated action and the truncated quantized action do not commute at all.
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.
NASA Astrophysics Data System (ADS)
Allanach, Ben; Biswas, Sanjoy; Mondal, Subhadeep; Mitra, Manimala
2015-01-01
A recent CMS search for the right-handed gauge boson WR reports an interesting deviation from the Standard Model. The search has been conducted in the e e j j channel and has shown a 2.8 σ excess around me e j j˜2 TeV . In this work, we explain the reported CMS excess with R -parity violating supersymmetry. We consider resonant selectron and sneutrino production, followed by the three body decays of the neutralino and chargino via an R -parity violating coupling. We fit the excess for slepton masses around 2 TeV. The scenario can further be tested in neutrinoless double beta decay (0 ν β β ) experiments. GERDA Phase-II will probe a significant portion of the good-fit parameter space.
NASA Astrophysics Data System (ADS)
Tamura, Ryo; Tanaka, Shu
2013-11-01
We study the phase transition behavior of a frustrated Heisenberg model on a stacked triangular lattice by Monte Carlo simulations. The model has three types of interactions: the ferromagnetic nearest-neighbor interaction J1 and antiferromagnetic third nearest-neighbor interaction J3 in each triangular layer and the ferromagnetic interlayer interaction J⊥. Frustration comes from the intralayer interactions J1 and J3. We focus on the case that the order parameter space is SO(3)×C3. We find that the model exhibits a first-order phase transition with breaking of the SO(3) and C3 symmetries at finite temperature. We also discover that the transition temperature increases but the latent heat decreases as J⊥/J1 increases, which is opposite to the behavior observed in typical unfrustrated three-dimensional systems.
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.
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
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.
Magnetic correlations beyond the Heisenberg model in an Fe monolayer on Rh(0 0 1).
Deák, A; Palotás, K; Szunyogh, L; Szabó, I A
2015-04-15
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. PMID:25786735
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.
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)
Ixert, Dominik; Tischler, Tobias; Schmidt, Kai P.
2015-11-01
We use nonperturbative linked-cluster expansions to determine the ground-state energy per site of the spin-one Heisenberg model on the kagome lattice. To this end, a parameter is introduced allowing us to interpolate between a fully trimerized state and the isotropic model. The ground-state energy per site of the full graph decomposition up to graphs of six triangles (18 spins) displays a complex behavior as a function of this parameter close to the isotropic model which we attribute to divergencies of partial series in the graph expansion of quasi-1D unfrustrated chain graphs. More concretely, these divergencies can be traced back to a quantum critical point of the one-dimensional unfrustrated chain of coupled triangles. Interestingly, the reorganization of the nonperturbative linked-cluster expansion in terms of clusters with enhanced symmetry yields a ground-state energy per site of the isotropic two-dimensional model that is in quantitative agreement with other numerical approaches in favor of a spontaneous trimerization of the system. Our findings are of general importance for any nonperturbative linked-cluster expansion on geometrically frustrated systems.
NASA Astrophysics Data System (ADS)
Benton, Owen; Shannon, Nic
2015-10-01
Magnetic pyrochlore oxides, including the spin ice materials, have proved to be a rich field for the study of geometrical frustration in three dimensions. Recently, a new family of magnetic oxides has been synthesised in which half of the tetrahedra in the pyrochlore lattice are inflated relative to the other half, making an alternating array of small and large tetrahedra. These "breathing pyrochlore" materials such as LiGaCr4O8, LiInCr4O8, and Ba3Yb2Zn5O11 provide new opportunities in the study of frustrated magnetism. Here we provide an analytic theory for the ground state phase diagram and spin correlations for the minimal model of magnetism in breathing pyrochlores: a classical nearest neighbour Heisenberg model with different exchange coefficients for the two species of tetrahedra. We find that the phase diagram comprises a Coulombic spin liquid phase, a conventional ferromagnetic phase and an unusual antiferromagnetic phase with lines of soft modes in reciprocal space, stabilised by an order-by-disorder mechanism. We obtain a theory of the spin correlations in this model using the self consistent Gaussian approximation (SCGA) which enables us to discuss the development of correlations in breathing pyrochlores as a function of temperature, and we quantitatively characterise the thermal crossover from the limit of isolated tetrahedra to the strongly correlated limit of the problem. We compare the results of our analysis with the results of recent neutron scattering experiments on LiInCr4O8.
NASA Astrophysics Data System (ADS)
Si, Qimiao; Goswami, Pallab
2014-03-01
Heavy fermion systems represent a prototypical setting to study magnetic quantum phase transitions. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum non-linear sigma model, and show that the skyrmion defects of the antiferromagnetic order parameter host a number of competing order parameters. In addition to the spin Peierls, charge and current density wave order parameters, we identify for the first time Kondo singlets as the competing dual orders of the antiferromagnetism, which can be related to each other via generalized chiral transformations of the underlying fermions. We also show that the conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the Néel order, which cancels the Berry phase of the local moments. Our results demonstrate the competition between the Kondo-singlet formation and spin-Peierls order when the antiferromagnetic order is suppressed, thereby shedding new light on the global phase diagram of heavy fermion systems at zero temperature. NSF.
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.
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)
I Dream of J.J., or Affordances and Motion Pictures.
ERIC Educational Resources Information Center
Anderson, Joseph D.
1995-01-01
Categorizes attempts to account for how viewers garner meanings from motion pictures as either semiotic, realist, or conventionalist. Proposes an alternative explanation based on J. J. Gibson's ecological theory of perception. Offers his concept of "affordances" as the key to an explanation of how meanings in motion pictures are generated and…
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.
Resonant slepton production yields CMS e e j j and e p Tj j excesses
NASA Astrophysics Data System (ADS)
Allanach, Ben; Biswas, Sanjoy; Mondal, Subhadeep; Mitra, Manimala
2015-01-01
Recent CMS searches for dileptoquark production report local excesses of 2.4 σ in an e e j j channel and 2.6 σ in an e p Tj j channel. Here, we simultaneously explain both excesses with resonant slepton production in R -parity violating supersymmetry. We consider resonant slepton production, which decays to a lepton and a chargino/neutralino, followed by three-body decays of the neutralino/chargino via an R -parity violating coupling. There are regions of parameter space which are also compatible at the 95% confidence level with a 2.8 σ e e j j excess in a recent CMS WR search, while being compatible with other direct search constraints. Phase II of the GERDA neutrinoless double beta decay (0 ν β β ) experiment will probe a sizable portion of the good-fit region.
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.
SWAP operation in the two-qubit Heisenberg XXZ model: Effects of anisotropy and magnetic field
Zhou Yue; Yang Fuhua; Feng Songlin; Zhang Guofeng
2007-06-15
In this paper we study the SWAP operation in a two-qubit anisotropic XXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter {lambda} within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.
Order by disorder in Kitaev-Heisenberg models on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Perkins, Natalia; Sizyuk, Yuriy; Ducatman, Samuel; Woelfle, Peter
Recent diffuse magnetic x-ray scattering data in Na2IrO3 clearly determined the spin orientation in this zigzag state and showed that, unexpectedly, it is along the 44.3 degrees direction with respect to a axis, which is approximately half way in between the cubic x and y axes. This experiment provides an important check of the validity of any model proposed to described the magnetic properties of Na2IrO3 as the model should correctly predict not only the type of the magnetic order but also its orientation in space. We propose that order by disorder mechanism in quantum J1-K1-J2-K2-J3 model gives the experimentally observed direction along cubic face diagonals. Our findings are based on both the calculation of the contribution of thermal fluctuations of quantum spins into free energy obtained by Hubbard-Stratonovich transformation and the zero-point correction to the ground state energy due to quantum spin fluctuations obtained by the spin-wave expansion at zero temperature. Nsf Grant DMR-1511768.
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)
Barón, MáXimo
1996-06-01
During the 1890s many facts regarding the nature of the atom emerged, the most important being that the atom was composed of even smaller particles. Theoretical and experimental discoveries of the time led to the identification of the first subatomic corpuscle, as J. J. Thomson originally called the electron. The measurement of it's e/m ratio, as well as of the properties of cathode rays, opened up a new perspective of the atom and helped to understand several then unexplained phenomena (e.g., atomic spectra). Reluctant to adopt a planetary view, Thomson deliberately chose an electromagnetic approach that has invoked the image of plum puddings and raisin muffins. Although Thomson's model was unsatisfactory for many reasons, it paved the way for Rutherford, one of his brilliant co-workers.
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)
Gong, Shoushu; Zhu, Wei; Balents, Leon; Sheng, Dongning
2015-03-01
We studied the extended spin- 1 / 2 kagome model with the first neighbor (J1), the second (J2) and third neighbor (J3) couplings using density matrix renormalization group. We established a quantum phase diagram for 0 <= J 2 <= 0 . 25J1 and 0 <=J3 <=J1 , where we find a q = (0 , 0) Neel phase, a chiral spin liquid (CSL), a cuboc1 phase that breaks both time-reversal and spin rotational symmetries, and a valence-bond solid at the neighbor of the Heisenberg model, where a possible Z2 spin liquid has been previously identified. Interestingly, the classical cuboc1 phase could survive in the spin- 1 / 2 system with strong quantum fluctuations, and the CSL emerges between the q = (0 , 0) and the cuboc1 phases. We discover that the CSL has the short spin correlation pattern consistent with the cuboc1 phase, but the chiral order structure is totally different. The CSL might be understood as a result of the competitions between the q = (0 , 0) and the cuboc1 phases in the presence of strong quantum fluctuations. We further studied the quantum phase transitions from the CSL to the magnetically ordered phases, and to the possible Z2 spin liquid of the Heisenberg kagome model. Interestingly, the exotic continuous topological phase transition might be realized in the system.
NASA Astrophysics Data System (ADS)
Rao, Wen-Jia; Zhang, Guang-Ming; Yang, Kun
2016-03-01
Applying a symmetric bulk bipartition to the one-dimensional Affleck-Kennedy-Lieb-Tasaki valence-bond solid (VBS) states for the integer spin-S Haldane gapped phase, we can create an array of fractionalized spin-S /2 edge states with the super unit cell l in the reduced bulk system, and the topological properties encoded in the VBS wave functions can be revealed. The entanglement Hamiltonian (EH) with even l corresponds to the quantum antiferromagnetic Heisenberg spin-S /2 model. For the even integer spins, the EH still describes the Haldane gapped phase. For the odd integer spins, however, the EH just corresponds to the quantum antiferromagnetic Heisenberg half-odd integer-spin model with spinon excitations, characterizing the critical point separating the topological Haldane phase from the trivial gapped phase. Our results thus demonstrate that the topological bulk property not only determines its fractionalized edge states but also the quantum criticality associated with the topological phase, where the elementary excitations are precisely those fractionalized edge degrees of freedom confined in the bulk of the topological phase.
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
Spatially anisotropic Heisenberg kagome antiferromagnet
NASA Astrophysics Data System (ADS)
Apel, W.; Yavors'kii, T.; Everts, H.-U.
2007-04-01
In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies (Hiroi et al 2001 J. Phys. Soc. Japan 70 3377; Fukaya et al 2003 Phys. Rev. Lett. 91 207603; Bert et al 2004 J. Phys.: Condens. Matter 16 S829; Bert et al 2005 Phys. Rev. Lett. 95 087203). It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the {\\mathrm {Sp}}(\\mathcal {N}) symmetric generalization of this model in the large \\mathcal {N} limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long-range order and a decoupled chain phase emerges.
NASA Astrophysics Data System (ADS)
Yu, Rong; Si, Qimiao
2015-09-01
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.
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
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.
Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice
NASA Astrophysics Data System (ADS)
Isaev, Leonid; Ortiz, Gerardo; Dukelsky, Jorge
2009-03-01
We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighbouring N'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N'eel and columnar phases. Our results suggest that the quantum phase transition between N'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice
NASA Astrophysics Data System (ADS)
Isaev, L.; Ortiz, G.; Dukelsky, J.
2009-01-01
We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry-preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers, and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighboring Néel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Néel and columnar phases. Our results suggest that the quantum phase transition between Néel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Goswami, Pallab; Si, Qimiao
2014-01-01
Heavy-fermion systems represent a prototypical setting to study magnetic quantum phase transitions. A particular focus has been on the physics of Kondo destruction, which captures quantum criticality beyond the Landau framework of order-parameter fluctuations. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo-destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum nonlinear sigma model, and show that the skyrmion defects of the antiferromagnetic order parameter host a number of competing order parameters. In addition to the spin Peierls, charge and current density wave order parameters, we identify for the first time Kondo singlets as the competing orders of the antiferromagnetism. We show that the antiferromagnetism and various competing singlet orders can be related to each other via generalized chiral transformations of the underlying fermions. We also show that the conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the Néel order, which cancels the Berry phase of the local moments. Our results demonstrate the competition between the Kondo singlet formation and spin-Peierls order when the antiferromagnetic order is suppressed, thereby shedding new light on the global phase diagram of heavy-fermion systems at zero temperature.
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)
Doretto, R. L.
2014-03-01
We study the plaquette valence-bond solid phase of the spin-1/2J1-J2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S =1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J1-J2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996), 10.1103/PhysRevB.54.9007] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34
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.
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.
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.
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.
Galois Symmetries of Bethe Parameters for the Heisenberg Pentagon
NASA Astrophysics Data System (ADS)
Banaszak, G.; Lulek, B.; Lulek, T.; Milewski, J.; Szydło, B.
2013-04-01
In this paper the field generated by the Bethe parameters related to the XXX model for the Heisenberg pentagon is considered. For the interior of the Brillouin zone, the Galois group of the Bethe number field over the rationals is determined. This Galois group is recognized as the group of arithmetic symmetries of the Bethe parameters.
Heisenberg uncertainty in reduced power algebras
NASA Astrophysics Data System (ADS)
Rosinger, Elemér E.
2012-12-01
The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far wider frameworks of scalars, namely, within one or the other of the infinitely many reduced power algebras which can replace the usual real numbers R, or complex numbers C. Three possible major advantages in Physics of such a reformulation are: 1) the disappearance of the well known and hard to deal with problem of the so called "infinities in Physics", 2) the possibilitiy to have infinitely many "levels of precision" instead of the only one existing at present, 3) the possibility to model "hierarchies of Planck constants", [2]. Last and not least, the scalars given by reduced power algebras contain as a particular case those obtained by Nonstandard Analysis, yet they are far more simple and easy to deal with, being in fact on the level of a first course in Algebra. A detailed version of this paper can be found in arxiv:0901.4825.
NASA Astrophysics Data System (ADS)
Eichten, Estia
2011-04-01
More than a quarter century ago, theoretical issues with the Standard Model scalar boson sector inspired theorists to develop alternative models of electroweak symmetry breaking. The goal of the EHLQ study of hadron collider physics was to help determine the basic parameters of a supercollider that could distinguish these alternatives. Now we await data from the CMS and ATLAS experiments at CERN's Large Hadron Collider to solve this mystery. Does the Standard Model survive or, as theorists generally expect, does new physics appear (Strong Dynamics, SUSY, Extra Dimensions,...)? Even well into the LHC era it is likely that questions about the origin of fermion mass and mixings will remain and new physics will bring new puzzles. This time, the associated new scales are unknown. The opportunity to address new physics at a future multi-TeV lepton collider is briefly addressed.
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.
J. J. Sakurai Prize for Theoretical Particle Physics Talk: Partons, QCD, and Factorization
NASA Astrophysics Data System (ADS)
Soper, Davison
2009-05-01
Many important cross sections in high-energy collisions are analyzed using factorization properties. I review the nature of factorization, how it arose from the parton model, and current issues in its development. This talk will be coordinated with the one by Collins.
J. J. Sakurai Prize for Theoretical Particle Physics Talk: Hard scattering factorization in QCD
NASA Astrophysics Data System (ADS)
Collins, John
2009-05-01
Many important cross sections in high-energy collisions are analyzed using factorization properties. I review the nature of factorization, how it arose from the parton model, and current issues in its development. This talk will be coordinated with the one by Soper.
NASA Astrophysics Data System (ADS)
Altarelli, Guido
2012-03-01
The LHC results released so far have very much restricted the possible range for the Standard Model Higgs boson mass. Moreover some indications for a signal at a mass around 125 GeV have been found. At the same time, no clear evidence for new physics has emerged from the LHC data. We discuss the impact of these results on our understanding of particle physics. The presently allowed window for the Higgs mass and the negative results for exotic particles are compatible with both the Standard model and its Supersymmetric extensions but imply considerable restrictions and need a substantial amount of fine tuning in all cases. We discuss the options that remain open and the perspectives for the near future.
J.J. Sakurai Prize Talk: Precision measurements and New Physics
NASA Astrophysics Data System (ADS)
Marciano, William
2002-04-01
The Standard Model of strong and electroweak interactions is a renormalizable quantum field theory. In that framework, quantum corrections to observables can be calculated with extraordinary accuracy. Comparison of those predictions with precision experimental measurements tests the theory and probes for small deviations from new physics effects. Recent examples of such tests and their implications will be described and the outlook for future advances will be discussed.
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.
J.J. Sakurai Prize for Theoretical Particle Physics: 40 Years of Lattice QCD
NASA Astrophysics Data System (ADS)
Lepage, Peter
2016-03-01
Lattice QCD was invented in 1973-74 by Ken Wilson, who passed away in 2013. This talk will describe the evolution of lattice QCD through the past 40 years with particular emphasis on its first years, and on the past decade, when lattice QCD simulations finally came of age. Thanks to theoretical breakthroughs in the late 1990s and early 2000s, lattice QCD simulations now produce the most accurate theoretical calculations in the history of strong-interaction physics. They play an essential role in high-precision experimental studies of physics within and beyond the Standard Model of Particle Physics. The talk will include a non-technical review of the conceptual ideas behind this revolutionary development in (highly) nonlinear quantum physics, together with a survey of its current impact on theoretical and experimental particle physics, and prospects for the future. Work supported by the National Science Foundation.
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
Heisenberg antiferromagnet on the Husimi lattice
NASA Astrophysics Data System (ADS)
Liao, H. J.; Xie, Z. Y.; Chen, J.; Han, X. J.; Xie, H. D.; Normand, B.; Xiang, T.
2016-02-01
We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on projected entangled simplex states. The nature of the ground state varies strongly with the spin quantum number S . For S =1/2 , it is an algebraic (gapless) quantum spin liquid. For S =1 , it is a gapped, nonmagnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For S =2 , it is a simplex-solid state with a spin gap and no symmetry breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For S =3/2 , and indeed for all spin values S ≥5/2 , the ground states have 120∘ antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of S , there is always a plateau in the magnetization at m =1/3 .
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...
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.
Quantum states for Heisenberg limited interferometry
NASA Astrophysics Data System (ADS)
Uys, Hermann; Meystre, Pierre
2007-06-01
An important aspect of quantum metrology is the engineering of quantum states with which to achieve Heisenberg limited measurement precision. In this limit the measurement uncertainty is inversely proportional to the number of interfering particles, N, a 1/√N improvement over the standad quantum limit. We have used numerical global optimization strategies to systematically search for quantum interferometer input states that achieve Heisenberg limited uncertainty in estimates of the interferometer phase shift. We compare the performance of candidates so obtained with that of non-classical states already known to yield Heisenberg limited uncertainty.
Quantum states for Heisenberg-limited interferometry
NASA Astrophysics Data System (ADS)
Uys, H.; Meystre, P.
2007-07-01
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/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.
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.
Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet
NASA Astrophysics Data System (ADS)
Zaletel, Michael P.; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R.
2016-05-01
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.
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.
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
Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains
NASA Astrophysics Data System (ADS)
Wang, Lihua; Chung, Sung Gong
2012-11-01
A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy λ and magnetic field B. To demonstrate its accuracy, we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg model, and find that EPT successfully reproduces the exact Bethe ansatz results for the ground state energy, the local magnetization, and the spin correlation functions (Bethe ansatz result is available for the first seven lattice separations). In particular, EPT confirms for the first time the asymptotic behavior of the spin correlation functions predicted by the conformal field theory, which realizes only for lattice separations larger than 1000. Next, turning on the z-axis anisotropy and the magnetic field, the 2- and 4-spin correlation functions are calculated, and the results are compared with those obtained by bosonization and density matrix renormalization group methods. Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state phase diagram in λ space is determined by Roomany--Wyld renormalization group (RG) finite size scaling. The results are in good agreement with those obtained by the level-spectroscopy method.
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.
NASA Astrophysics Data System (ADS)
Sjostrand, Torbjorn
2012-03-01
The nature of observable events at the LHC is mainly determined by QCD physics, i.e. strong interactions. The search for new physics obviously implies a desire to go beyond QCD. Nevertheless, also in cases where non-QCD processes are studied, new aspects of QCD physics may enter the back door. We here give three examples: decays with R-parity violation in SUSY, the formation of long-lived R-hadrons in SUSY, and parton showers and hadronization in Hidden Valley scenarios. These three possibilities have been implemented in the general-purpose PYTHIA event generator, so that detailed studies of consequences can be performed.
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.
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)
Excitations in a Four-Leg Antiferromagnetic Heisenberg Spin Tube,
Garlea, Vasile O; Zheludev, Andrey I; Regnault, L.-P.; Chung, J.-H.; Qiu, Y.; Boehm, Martin; Habicht, Klaus; Meissner, Michael; Fernandez-Baca, Jaime A
2008-01-01
Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu2Cl4 D8C4SO2. Contrary to previously conjectured models that relied on bond-alternating nearest-neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S 1=2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.
Excitations in a four-leg antiferromagnetic Heisenberg spin tube
Garlea, Vasile O; Zheludev, Andrey I; Regnault, L.-P.; Chung, J.-H.; Qiu, Y.; Boehm, Martin; Habicht, Klaus; Meissner, Michael
2008-01-01
Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu$_2$Cl$_{4}\\cdot$ D$_8$C$_4$SO$_2$. Contrary to previously conjectured models that relied on bond-alternating nearest neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a $S=1/2$ 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.
Quantum localization in bilayer Heisenberg antiferromagnets with site dilution.
Roscilde, Tommaso; Haas, Stephan
2005-11-11
The field-induced antiferromagnetic ordering in systems of weakly coupled S = 1/2 dimers at zero temperature can be described as a Bose-Einstein condensation of triplet quasiparticles (singlet quasiholes) in the ground state. For the case of a Heisenberg bilayer, it is here shown how the above picture is altered in the presence of site dilution of the magnetic lattice. Geometric randomness leads to quantum localization of the quasiparticles or quasiholes and to an extended Bose-glass phase in a realistic disordered model. This localization phenomenon drives the system towards a quantum-disordered phase well before the classical geometric percolation threshold is reached. PMID:16384096
Entanglement of Two-Qubit Quantum Heisenberg XYZ Chain
NASA Astrophysics Data System (ADS)
Xi, Xiao-Qiang; Hao, San-Ru; Chen, Wen-Xue; Yue, Rui-Hong
2002-08-01
We derive the analytic expression of the concurrence in the quantum Heisenberg XYZ model and discuss the influence of parameters J, Δ and Γ on the concurrence. By choosing different values of Γ and Δ, we obtain the XX, XY, XXX and XXZ chains. The concurrence decreases with increasing temperature. When T→0, the concurrence reaches its maximum value 1, i.e. the entangled state, |Ψ> = (((2)1/2)/2)(|01>-|10>), is maximum entanglement. For the XXZ chain, when Γ→∞, the concurrence will meet its maximum value Cmax = (sinh (1/T))/(cosh (1/T)).
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.
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. PMID:26551137
NASA Astrophysics Data System (ADS)
Abgaryan, V. S.; Ananikian, N. S.; Ananikyan, L. N.; Hovhannisyan, V.
2015-02-01
Thermal entanglement, magnetic and quadrupole moments properties of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on a diamond chain are considered. Magnetization and quadrupole moment plateaus are observed for the antiferromagnetic couplings. Thermal negativity as a measure of quantum entanglement of the mixed spin system is calculated. Different behavior for the negativity is obtained for the various values of Heisenberg dipolar and quadrupole couplings. The intermediate plateau of the negativity has been observed at the absence of the single-ion anisotropy and quadrupole interaction term. When dipolar and quadrupole couplings are equal there is a similar behavior of negativity and quadrupole moment.
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.
On moments-based Heisenberg inequalities
NASA Astrophysics Data System (ADS)
Zozor, Steeve; Portesi, Mariela; Sanchez-Moreno, Pablo; Dehesa, Jesus S.
2011-03-01
In this paper we revisit the quantitative formulation of the Heisenberg uncertainty principle. The primary version of this principle establishes the impossibility of refined simultaneous measurement of position x and momentum u for a (1-dimensional) quantum particle in terms of variances: <‖x‖2><‖u‖2>⩾1/4. Since this inequality applies provided each variance exists, some authors proposed entropic versions of this principle as an alternative (employing Shannon's or Rényi's entropies). As another alternative, we consider moments-based formulations and show that inequalities involving moments of orders other than 2 can be found. Our procedure is based on the Rényi entropic versions of the Heisenberg relation together with the search for the maximal entropy under statistical moments' constraints (<‖x‖a> and <‖u‖b>). Our result improves a relation proposed very recently by Dehesa et al.. [1] where the same approach was used but starting with the Shannon version of the entropic uncertainty relation. Furthermore, we show that when a =b, the best bound we can find with our approach coincides with that of Ref. [1] and, in addition, for a = b = 2 the variance-based Heisenberg relation is recovered. Finally, we illustrate our results in the cases of d-dimensional hydrogenic systems.
Even-odd effect in short antiferromagnetic Heisenberg chains
NASA Astrophysics Data System (ADS)
Machens, A.; Konstantinidis, N. P.; Waldmann, O.; Schneider, I.; Eggert, S.
2013-04-01
Motivated by recent experiments on chemically synthesized magnetic molecular chains, we investigate the lowest-lying energy band of short spin-s antiferromagnetic Heisenberg chains focusing on effects of open boundaries. By numerical diagonalization we find that the Landé pattern in the energy levels, i.e., E(S)∝S(S+1) for total spin S, known from, e.g., ring-shaped nanomagnets, can be recovered in odd-membered chains, while strong deviations are found for the lowest excitations in chains with an even number of sites. This particular even-odd effect in the short Heisenberg chains cannot be explained by simple effective Hamiltonians and symmetry arguments. We go beyond these approaches, taking into account quantum fluctuations by means of a path-integral description and the valence bond basis, but the resulting quantum edge-spin picture which is known to work well for long chains does not agree with the numerical results for short chains and cannot explain the even-odd effect. Instead, by analyzing also the classical chain model, we show that spatial fluctuations dominate the physical behavior in short chains, with length N≲eπs, for any spin s. Such short chains are found to display a unique behavior, which is not related to the thermodynamic limit and cannot be described well by theories developed for this regime.
NASA Astrophysics Data System (ADS)
Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiang-Gang
We study this model using the cluster update algorithm for tensor product states (TPSs). We find that the ground state energies at finite sizes and in the thermodynamic limit are in good agreement with the exact diagonalization study. At the largest bond dimension available D = 9 and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point J2c1 = 0 . 53 (1) J1 and the critical exponents β = 0 . 50 (4) . In the intermediate region we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation. By fitting a universal scaling function for the spin-spin correlation we find the critical exponents ν = 0 . 68 (3) and ηs = 0 . 34 (6) , which is very close to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at J2c1 = 0 . 53 (1) J1 . This project is supported by the EU Strep project QUEVADIS, the ERC Grant QUERG, and the FWF SFB Grants FoQuS and ViCoM; and the Institute for Quantum Information and Matter.
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.
Zero temperature phase transitions in quantum Heisenberg ferromagnets
Sachdev, S.; Senthil, T.
1996-10-01
The purpose of this work is to understand the zero temperature phases and the phase transitions of Heisenberg spin systems which can have an extensive, spontaneous magnetic moment, this entails a study of quantum transitions with an order parameter which is also a non-abelian conserved charge. To this end, we introduce and study a new class of lattice models of quantum rotors. We compute their mean-field phase diagrams and present continuum, quantum field-theoretic descriptions of their low energy properties in different regimes. We argue that, in spatial dimension {ital d}=1, the phase transitions in itinerant Fermi systems are in the same universality class as the corresponding transitions in certain rotor models. We discuss implications of our results for itinerant fermions systems in higher {ital d} and for other physical systems. Copyright {copyright} 1996 Academic Press, Inc.
Heisenberg algebra, umbral calculus and orthogonal polynomials
Dattoli, G.; Levi, D.; Winternitz, P.
2008-05-15
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation [P,M]=1. In ordinary quantum mechanics, P is the derivative and M the coordinate operator. Here, we shall realize P as a second order differential operator and M as a first order integral one. We show that this makes it possible to solve large classes of differential and integrodifferential equations and to introduce new classes of orthogonal polynomials, related to Laguerre polynomials. These polynomials are particularly well suited for describing the so-called flatenned beams in laser theory.
Generalized Weyl-Heisenberg (GWH) groups
NASA Astrophysics Data System (ADS)
Ghaani Farashahi, Arash
2014-09-01
Let be a locally compact group, be a locally compact Abelian (LCA) group, be a continuous homomorphism, and let be the semi-direct product of and with respect to the continuous homomorphism . In this article, we introduce the Generalized Weyl-Heisenberg (GWH) group associate with the semi-direct product group . We will study basic properties of from harmonic analysis aspects. Finally, we will illustrate applications of these methods in the case of some well-known semi-direct product groups.
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.
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 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.
Heisenberg groups and noncommutative fluxes
NASA Astrophysics Data System (ADS)
Freed, Daniel S.; Moore, Gregory W.; Segal, Graeme
2007-01-01
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 Z2-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 (4 k + 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.
Quantum rms error and Heisenberg's error-disturbance relation
NASA Astrophysics Data System (ADS)
Busch, Paul
2014-09-01
Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, a Heisenberg-type tradeoff relation for joint measurements of position and momentum has been formulated and proven in [Phys. Rev. Lett. 111, 160405 (2013)]. Here I show how the apparent conflict is resolved by a careful consideration of the quantum generalization of the notion of root-mean-square error. The claim of a violation of Heisenberg's principle is untenable as it is based on a historically wrong attribution of an incorrect relation to Heisenberg, which is in fact trivially violated. We review a new general trade-off relation for the necessary errors in approximate joint measurements of incompatible qubit observables that is in the spirit of Heisenberg's intuitions. The experiments mentioned may directly be used to test this new error inequality.
NASA Astrophysics Data System (ADS)
Gurr, Henry
2014-03-01
Princeton Physicist J. J. Hopfield's Mathematical Model of the Mammalian Brain, (Similar To Ising Glass Model of a crystal of magnetic spin particles) says our Brain-Work for Memory, Perception, Language, Thinking, etc, (Even the AHA-EUREKA-Flash Of Insight Type Problem Solving), is achieved by our massively inter-connected CNS Neurons ... working together ... MINIMIZING an analog of physical energy ... thus yielding Optimal Solutions: These ``best'' answers, correspond to highest mental coherence, for most facets organism response, beit mental (eg: perception, memory, ideas, thinking, etc) or physical-muscular-actions (eg speaking, tool using, trail following, etc). Our brain is this way, because living creature, MUST be evolved, so they will find & use the best actions, for survival!!! Our human heritage, is to instantly compute near optimal future plans, (mental & physical-muscular), and be able to accomplish plans reliably & efficiently. If you know of book or articles in these topic areas, please email to HenryG--USCA.edu How to work well, with your own ``self'', called mind-body, will follow!! Conjectures: Who is the ``I'' that appears to make decisions? Am ``I'' the master of my domain? Is there an ``I'' or am ``I'' merely an illusion of reality.
NASA Astrophysics Data System (ADS)
Webber, Bryan
2012-03-01
Comparing theoretical predictions with experimental data on particle collisions like those at the Large Hadron Collider is far from straightforward. The predictions usually concern fundamental objects (quarks, gluons, leptons, ) whereas the colliding hadrons are complicated bound states. Furthermore, final states of interest often contain high-energy jets of many hadrons, together with underlying lower-energy hadron production. The jets may come from primary interactions producing energetic quarks and gluons, or from the decays of heavy or highly boosted objects, possibly new forms of matter. I will discuss the development of computer simulations of jet production in hard collisions, and of jet-finding algorithms that aim to reconstruct the fundamental collision and decay dynamics from hadronic final states. In both cases, improvements in the underlying theoretical framework have led to a better description of Standard Model processes at the LHC, and better tools for the discovery of any new processes that may lie within its reach.
Proof of Heisenberg's Error-Disturbance Relation
NASA Astrophysics Data System (ADS)
Busch, Paul; Lahti, Pekka; Werner, Reinhard F.
2013-10-01
While the slogan “no measurement without disturbance” has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [L. Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum. Measures of error and disturbance are here defined as figures of merit characteristic of measuring devices. As such they are state independent, each giving worst-case estimates across all states, in contrast to previous work that is concerned with the relationship between error and disturbance in an individual state.
Proof of Heisenberg's error-disturbance relation.
Busch, Paul; Lahti, Pekka; Werner, Reinhard F
2013-10-18
While the slogan "no measurement without disturbance" has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [L. Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum. Measures of error and disturbance are here defined as figures of merit characteristic of measuring devices. As such they are state independent, each giving worst-case estimates across all states, in contrast to previous work that is concerned with the relationship between error and disturbance in an individual state. PMID:24182239
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
The elusive Heisenberg limit in quantum-enhanced metrology
NASA Astrophysics Data System (ADS)
Demkowicz-Dobrzański, Rafał; Kołodyński, Jan; Guţă, Mădălin
2012-09-01
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.
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
Spin-wave multiple excitations in nanoscale classical Heisenberg antiferromagnets
Hou, Zhuofei; Landau, David P; Stocks, George Malcolm; Brown, G.
2015-01-01
Monte Carlo and spin dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic latticewith linear sizesL 40 at a temperature below the N eel temperature. Nanoparticles are modeled with completely free boundary conditions, i.e., six free surfaces, and nanofilms are modeled with two free surfaces in the spatial z direction and periodic boundaries parallel to the surfaces in the xy direction, which are compared to the infinite system with periodic boundary conditions. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion formore » individual spins using a fast spin dynamics algorithm with the fourth-order Suzuki-Trotter decomposition of exponential operators, with initial spin configurations generated by Monte Carlo simulations. The local dynamic structure factor S(q, ) was calculated from the local space- and time-displaced spin-spin correlation function. Multiple excitation peaks for wave vectors within the first Brillouin zone appear in the spin-wave spectra of the transverse component of dynamic structure factor ST (q, ) in the nanoscale classical Heisenberg antiferromagnet, which are lacking if periodic boundary conditions are used. With the assumption of q-space spin-wave reflections with broken momentum conservation due to free-surface confinements, we successfully explained those spectra quantitatively in the linear dispersion region. Meanwhile, we also observed two unexpected quantized spin-wave excitation modes in the spatial z direction in nanofilms for ST (q, ) not expected in bulk systems. The results of this study indicate the presence of unexpected forms of spin-wave excitation behavior that have yet to be observed experimentally but could be directly tested through neutron scattering experiments on nanoscale RbMnF3 particles or films.« less
Spin-wave multiple excitations in nanoscale classical Heisenberg antiferromagnets
Hou, Zhuofei; Landau, David P; Stocks, George Malcolm; Brown, G.
2015-01-01
Monte Carlo and spin dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic latticewith linear sizesL 40 at a temperature below the N eel temperature. Nanoparticles are modeled with completely free boundary conditions, i.e., six free surfaces, and nanofilms are modeled with two free surfaces in the spatial z direction and periodic boundaries parallel to the surfaces in the xy direction, which are compared to the infinite system with periodic boundary conditions. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a fast spin dynamics algorithm with the fourth-order Suzuki-Trotter decomposition of exponential operators, with initial spin configurations generated by Monte Carlo simulations. The local dynamic structure factor S(q, ) was calculated from the local space- and time-displaced spin-spin correlation function. Multiple excitation peaks for wave vectors within the first Brillouin zone appear in the spin-wave spectra of the transverse component of dynamic structure factor ST (q, ) in the nanoscale classical Heisenberg antiferromagnet, which are lacking if periodic boundary conditions are used. With the assumption of q-space spin-wave reflections with broken momentum conservation due to free-surface confinements, we successfully explained those spectra quantitatively in the linear dispersion region. Meanwhile, we also observed two unexpected quantized spin-wave excitation modes in the spatial z direction in nanofilms for ST (q, ) not expected in bulk systems. The results of this study indicate the presence of unexpected forms of spin-wave excitation behavior that have yet to be observed experimentally but could be directly tested through neutron scattering experiments on nanoscale RbMnF3 particles or films.
Spin-wave multiple excitations in nanoscale classical Heisenberg antiferromagnets
NASA Astrophysics Data System (ADS)
Hou, Zhuofei; Landau, D. P.; Stocks, G. M.; Brown, G.
2015-02-01
Monte Carlo and spin dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic lattice with linear sizes L ⩽40 at a temperature below the Néel temperature. Nanoparticles are modeled with completely free boundary conditions, i.e., six free surfaces, and nanofilms are modeled with two free surfaces in the spatial z direction and periodic boundaries parallel to the surfaces in the x y direction, which are compared to the "infinite" system with periodic boundary conditions. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a fast spin dynamics algorithm with the fourth-order Suzuki-Trotter decomposition of exponential operators, with initial spin configurations generated by Monte Carlo simulations. The local dynamic structure factor S (q ,ω ) was calculated from the local space- and time-displaced spin-spin correlation function. Multiple excitation peaks for wave vectors within the first Brillouin zone appear in the spin-wave spectra of the transverse component of dynamic structure factor ST(q ,ω ) in the nanoscale classical Heisenberg antiferromagnet, which are lacking if periodic boundary conditions are used. With the assumption of q -space spin-wave reflections with broken momentum conservation due to free-surface confinements, we successfully explained those spectra quantitatively in the linear dispersion region. Meanwhile, we also observed two unexpected quantized spin-wave excitation modes in the spatial z direction in nanofilms for ST(q ,ω ) not expected in bulk systems. The results of this study indicate the presence of unexpected forms of spin-wave excitation behavior that have yet to be observed experimentally but could be directly tested through neutron scattering experiments on nanoscale RbMnF3 particles or films.
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.
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.
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
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)
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.
Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
NASA Astrophysics Data System (ADS)
Wierschem, Keola; Sengupta, Pinaki
2014-12-01
We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional (Q1D) geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean-field universality of the critical coupling times the coordination number of the lattice. Inspired by recent developments in the characterization of symmetry protected topological (SPT) states, of which the Haldane phase of the spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we provide direct evidence that the Q1D Haldane phase is indeed a nontrivial SPT state.
NASA Astrophysics Data System (ADS)
Hoffmann, Tim
2000-01-01
The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schrödinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izgerin and Korepin. Moreover a doubly discrete IHM is presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.
Linear dependencies in Weyl-Heisenberg orbits
NASA Astrophysics Data System (ADS)
Dang, Hoan Bui; Blanchfield, Kate; Bengtsson, Ingemar; Appleby, D. M.
2013-11-01
Five years ago, Lane Hughston showed that some of the symmetric informationally complete positive operator valued measures (SICs) in dimension 3 coincide with the Hesse configuration (a structure well known to algebraic geometers, which arises from the torsion points of a certain elliptic curve). This connection with elliptic curves is signalled by the presence of linear dependencies among the SIC vectors. Here we look for analogous connections between SICs and algebraic geometry by performing computer searches for linear dependencies in higher dimensional SICs. We prove that linear dependencies will always emerge in Weyl-Heisenberg orbits when the fiducial vector lies in a certain subspace of an order 3 unitary matrix. This includes SICs when the dimension is divisible by 3 or equal to 8 mod 9. We examine the linear dependencies in dimension 6 in detail and show that smaller dimensional SICs are contained within this structure, potentially impacting the SIC existence problem. We extend our results to look for linear dependencies in orbits when the fiducial vector lies in an eigenspace of other elements of the Clifford group that are not order 3. Finally, we align our work with recent studies on representations of the Clifford group.
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.
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
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.
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
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.
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.
Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
NASA Astrophysics Data System (ADS)
Mazza, Paolo P.; Stéphan, Jean-Marie; Canovi, Elena; Alba, Vincenzo; Brockmann, Michael; Haque, Masudul
2016-01-01
The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.
Quantum computing with quantum dots using the Heisenberg exchange interaction
NASA Astrophysics Data System (ADS)
Dewaele, Nick J.
One of the most promising systems for creating a working quantum computer is the triple quantum dots in a linear semiconductor. One of the biggest advantages is that we are able to perform Heisenberg exchange gates on the physical qubits. These exchanges are both fast and relatively low energy. Which means that they would be excellent for producing fast and accurate operations. In order to prevent leakage errors we use a 3 qubit DFS to encode a logical qubit. Here we determine the theoretical time dependent affects of applying the Heisenberg exchange gates in the DFS basis as well as the effect of applying multiple exchange gates at the same time. we also find that applying two heisenberg exchange gates at the same time is an effective way of implementing a leakage elimination operator.
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.
Strong Coulomb effects in hole-doped Heisenberg chains
NASA Astrophysics Data System (ADS)
Schnack, J.
2005-06-01
Substances such as the “telephone number compound” Sr14Cu24O41 are intrinsically hole-doped. The involved interplay of spin and charge dynamics is a challenge for theory. In this article we propose to describe hole-doped Heisenberg spin rings by means of complete numerical diagonalization of a Heisenberg Hamiltonian that depends parametrically on hole positions and includes the screened Coulomb interaction among the holes. It is demonstrated that key observables like magnetic susceptibility, specific heat, and inelastic neutron scattering cross section depend sensitively on the dielectric constant of the screened Coulomb potential.
A survey of algebraic actions of the discrete Heisenberg group
NASA Astrophysics Data System (ADS)
Lind, D.; Schmidt, K.
2015-08-01
The study of actions of countable groups by automorphisms of compact Abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the simplest non-commutative example, where dynamical phenomena related to its non-commutativity already illustrate many of these connections. The explicit structure of this group means that these phenomena have concrete descriptions, which are not only instances of the general theory but are also testing grounds for further work. This paper surveys what is known about such actions of the discrete Heisenberg group, providing numerous examples and emphasizing many of the open problems that remain. Bibliography: 71 titles.
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.
Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD
NASA Astrophysics Data System (ADS)
Pérez-García, David; Tierz, Miguel
2014-04-01
By using random matrix models, we uncover a connection between the low-energy sector of four-dimensional QCD at finite volume and the Heisenberg XX model in a 1D spin chain. This connection allows us to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. For the spin chain, we predict a third-order phase transition and a Tracy-Widom law in the transition region. We also comment on possible numerical implications of the connection as well as on possible experimental implementations.
Spin-1/2 Heisenberg Antiferromagnet on the Spatially Anisotropic Kagome Lattice
NASA Astrophysics Data System (ADS)
Schnyder, Andreas; Starykh, Oleg; Balents, Leon
2008-03-01
We study the quasi-one-dimensional limit of the Spin-1/2 quantum antiferromagnet on the Kagome lattice, a model Hamiltonian that might be of relevance for the mineral volborthite [1,2]. The lattice is divided into antiferromagnetic spin-chains (exchange J) that are weakly coupled via intermediate ``dangling'' spins (exchange J'). Using bosonization, renormalization group methods, and current algebra techniques we determine the ground state as a function of J'/J. The case of a strictly one-dimensional Kagome strip is also discussed. [1] Z. Hiroi, M. Hanawa, N. Kobayashi, M. Nohara, Hidenori Takagi, Y. Kato, and M. Takigawa, J. Phys. Soc. Japan 70, 3377 (2001). [2] F. Bert, D. Bono, P. Mendels, F. Ladieu, F. Duc, J.-C. Trumbe, and P. Millet, Phys. Rev. Lett. 95, 087203 (2005).
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.
Spin-1 Heisenberg ferromagnet using pair approximation method
NASA Astrophysics Data System (ADS)
Mert, Murat; Kılıç, Ahmet; Mert, Gülistan
2016-06-01
Thermodynamic properties for Heisenberg ferromagnet with spin-1 on the simple cubic lattice have been calculated using pair approximation method. We introduce the single-ion anisotropy and the next-nearest-neighbor exchange interaction. We found that for negative single-ion anisotropy parameter, the internal energy is positive and heat capacity has two peaks.
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.
Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
NASA Astrophysics Data System (ADS)
Murmann, S.; Deuretzbacher, F.; Zürn, G.; Bjerlin, J.; Reimann, S. M.; Santos, L.; Lompe, T.; Jochim, S.
2015-11-01
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system.
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.
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.
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.
A second species of spinons in the S=1/2 Heisenberg antiferromagnet on kagome
NASA Astrophysics Data System (ADS)
Mellado, Paula; Hao, Zhihao; Tchernyshyov, Oleg
2010-03-01
The S=1/2 Heisenberg model on kagome can be viewed as an ensemble of spinons, fermionic quasiparticles with S=1/2 bound into small, heavy pairs whose binding energy sets the spin gap [1]. The apparent lack of a spin gap in real kagome magnets (e.g. herbertsmithite) may be associated with the Dzyaloshinskii-Moriya (DM) term D .(SixSj) in the Hamiltonian allowed by lattice symmetry. The DM term suppresses the spin gap and eventually induces long-range magnetic order [2]. A recent study [3] hints at the presence of an intermediate gapless phase without magnetic order. We propose that this phase arises as a result of condensation of a second spinon species (kinks). Here we study the motion of a single kink on the Husimi cactus, the analog of kagome in a hyperbolic plane. The kink is localized in the pure Heisenberg model and becomes mobile when D !=0. We calculate the one-particle density of states and the bandwidth. [1] Z. Hao and O. Tchernyshyov, Phys. Rev. Lett. 103, 187203 (2009). [2] O. C'epas et al., Phys. Rev. B 78, 140405 (2008). [3] I. Rousochatzakis et al., Phys. Rev. B 79, 214415 (2009).
Ternary Z3 -graded generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-04-01
We investigate a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, j = e 2πi/3, one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. A cubic analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator. A set of eigenstates in coordinate representation is constructed in terms of functions satisfying linear differential equation of third order.
Investigation of non-Hermitian Hamiltonians in the Heisenberg picture
NASA Astrophysics Data System (ADS)
Miao, Yan-Gang; Xu, Zhen-Ming
2016-05-01
The Heisenberg picture for non-Hermitian but η-pseudo-Hermitian Hamiltonian systems is suggested. If a non-Hermitian but η-pseudo-Hermitian Hamiltonian leads to real second order equations of motion, though their first order Heisenberg equations of motion are complex, we can construct a Hermitian counterpart that gives the same second order equations of motion. In terms of a similarity transformation we verify the iso-spectral property of the Hermitian and non-Hermitian Hamiltonians and obtain the related eigenfunctions. This feature can be used to determine real eigenvalues for such non-Hermitian Hamiltonian systems. As an application, two new non-Hermitian Hamiltonians are constructed and investigated, where one is non-Hermitian and non-PT-symmetric and the other is non-Hermitian but PT-symmetric. Moreover, the complementarity and compatibility between our treatment and the PT symmetry are discussed.
Euler-Heisenberg-Weiss action for QCD +QED
NASA Astrophysics Data System (ADS)
Ozaki, Sho; Arai, Takashi; Hattori, Koichi; Itakura, Kazunori
2015-07-01
We derive an analytic expression for one-loop effective action of QCD +QED at zero and finite temperatures by using the Schwinger proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic fields but also for the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED +QCD , and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this "Euler-Heisenberg-Weiss" action in QCD +QED , we investigate quark pair productions induced by QCD +QED fields at zero temperature and the Polyakov loop in the presence of strong electromagnetic fields. Quark one-loop contribution to the effective potential of the Polyakov loop explicitly breaks the center symmetry, and is found to be enhanced by the magnetic field, which is consistent with the inverse magnetic catalysis observed in lattice QCD simulation.
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 Astrophysics Data System (ADS)
Lau, Man-Hot; Dasgupta, Chandan
1989-04-01
The role of topological point defects (hedgehogs) in the phase transition of the classical Heisenberg model in three dimensions is investigated by using Monte Carlo simulations. Simulations of the behavior of the defects near the phase transition show that the number density of defects increases sharply and defect pairs with separations comparable to the sample size begin to appear as the temperature is increased through the transition temperature. In simulations in a restricted ensemble in which spin configurations containing defects are not allowed, the system appears to remain ordered at all temperatures. Simulations in which the spin-spin interaction is set equal to zero and the number density of defects is controlled by varying a ``chemical potential'' term indicate that the system is ordered if the number density of defect pairs is sufficiently small. These results show that topological defects play a crucial role in the three-dimensional Heisenberg transition in the sense that configurations containing defect pairs are necessary for the transition from the ferromagnetic to the paramagnetic phase to occur.
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.
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.
Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain
NASA Astrophysics Data System (ADS)
Weiße, A.; Wellein, G.; Fehske, H.
1999-09-01
As a simple model for spin-Peierls systems we study a frustrated Heisenberg chain coupled to optical phonons. In view of the anorganic spin-Peierls compound CuGeO3 we consider two different mechanisms of spin-phonon coupling. Combining variational concepts in the adiabatic regime and perturbation theory in the antiadiabatic regime we derive effective spin Hamiltonians which cover the dynamical effect of phonons in an approximate way. Ground-state phase diagrams of these models are determined, and the effect of frustration is discussed. Comparing the properties of the ground state and low-lying excitations with exact diagonalization data for the full quantum spin-phonon models, good agreement is found especially in the antiadiabatic regime.
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)
Xiao, Fan
The magnetic properties of a family of molecular-based quasi-two-dimensional S=1/2 Heisenberg antiferromagnets (2D QHAF) are studied. Three compounds, Cu(pz)2 (ClO4)2, Cu(pz)2(BF 4)2, and [Cu(pz)2(NO3)](PF6) contain similar planes of Cu2+ ions linked into magnetically square lattices by bridging pyrazine molecules (pz =C4H4N 2). The anions provide charge balance as well as isolation between the layers. Low field single crystal measurements of susceptibility and magnetization reveal low ratios of Neel temperatures to exchange strengths (4.25/17.5 = 0.243, 3.80/15.3 = 0.248, and 3.05/10.8 = 0.282, respectively) while the ratio of the anisotropy fields HA(kOe) to the saturation field HSAT(kOe) are small (2.6/490 = 5.3x10-3, 2.4/430 = 5.5x10-3, and 0.07/300 = 2.3x10-4, respectively), demonstrating close approximations to a two-dimensional Heisenberg model. The susceptibilities of Cu(pz)2(ClO4)2 and Cu(pz)2(BF4)2 show evidence of a spin crossover (Heisenberg to XY) at low temperatures; their zero-field ordering transitions are primarily driven by the XY behavior with the ultimate three-dimensional transition appearing parasitically. The [Cu(pz)2(NO 3)](PF6) compound remains Heisenberg-like at all temperatures, with its transition to the Neel state due to the inter- layer interactions. High field single crystal measurements of Cu(pz)2(ClO 4)2 indicates that both spin crossover transition temperature and ordering temperature increase as the external field increases up to 5 T. The results suggests a field-induced XY anisotropy is produced by the external field and the ordering temperature vs field follows a Berezinskii-Kosterlitz-Thouless (BKT)-like transition trend predicted by quantum Monte Carlo simulation. Calorimetry measurements were performed to verify the hypothesis with external fields up to 33 T. The results successfully confirmed our prediction. The transition temperature shows a rounded maximum at 16 T and starts dropping as the field gets stronger. The
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:
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.
Valence bond and von Neumann entanglement entropy in Heisenberg ladders.
Kallin, Ann B; González, Iván; Hastings, Matthew B; Melko, Roger G
2009-09-11
We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction. PMID:19792398
Pair approximation method for spin-1 Heisenberg system
NASA Astrophysics Data System (ADS)
Mert, Murat; Kılıç, Ahmet; Mert, Gülistan
2016-03-01
Spin-1 Heisenberg system on simple cubic lattice is considered in the pair approximation method assuming that the second-nearest-neighbor exchange interaction parameter has a negative value. The system is described in presence of an external magnetic field. The effects of the negative single-ion anisotropy and the negative second-nearest-neighbor exchange interaction on magnetization, internal energy, heat capacity, entropy and free energy are investigated. There are diverse anomalies at low temperature. In the magnetization and other thermodynamic quantities, the first-order phase transitions from ferromagnetic state to antiferromagnetic state and from ferromagnetic state to paramagnetic state have been observed.
Open Heisenberg chain under boundary fields: A magnonic logic gate
NASA Astrophysics Data System (ADS)
Landi, Gabriel T.; Karevski, Dragi
2015-05-01
We study the spin transport in the quantum Heisenberg spin chain subject to boundary magnetic fields and driven out of equilibrium by Lindblad dissipators. An exact solution is given in terms of matrix product states, which allows us to calculate exactly the spin current for any chain size. It is found that the system undergoes a discontinuous spin-valve-like quantum phase transition from ballistic to subdiffusive spin current, depending on the value of the boundary fields. Thus, the chain behaves as an extremely sensitive magnonic logic gate operating with the boundary fields as the base element.
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.
Quantum Correlations and Teleportation in Heisenberg XX Spin Chain
NASA Astrophysics Data System (ADS)
Qin, Wan; Guo, Jin-Liang
2015-07-01
We investigate the thermal quantum correlations in the Heisenberg XX spin chain, and the teleportation of a two-qubit entangled state via the spin chain is analyzed. It is found that the effects of external magnetic field and three-site interaction on the thermal entanglement and quantum discord between the nearest or the next nearest neighbor qubits behave differently in various aspects. Special attention is paid to how to enhance the quantum correlations of the output state and the average fidelity of the teleportation. We find that quantum discord gives a better performance in the quantum correlations transmission, and the three-site interaction is necessary for a successful teleportation.
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.
NASA Astrophysics Data System (ADS)
Searcy, Jacob; Huang, Lillian; Pleier, Marc-André; Zhu, Junjie
2016-05-01
The unitarization of the longitudinal vector boson scattering (VBS) cross section by the Higgs boson is a fundamental prediction of the Standard Model which has not been experimentally verified. One of the most promising ways to measure VBS uses events containing two leptonically decaying same-electric-charge W bosons produced in association with two jets. However, the angular distributions of the leptons in the W boson rest frame, which are commonly used to fit polarization fractions, are not readily available in this process due to the presence of two neutrinos in the final state. In this paper we present a method to alleviate this problem by using a deep machine learning technique to recover these angular distributions from measurable event kinematics and demonstrate how the longitudinal-longitudinal scattering fraction could be studied. We show that this method doubles the expected sensitivity when compared to previous proposals.
Stable transitivity of Heisenberg group extensions of hyperbolic systems
NASA Astrophysics Data System (ADS)
Niţică, Viorel; Török, Andrei
2014-04-01
We consider skew-extensions with fibre the standard real Heisenberg group { H}_n of a uniformly hyperbolic dynamical system. We show that among the Cr extensions (r > 0) that avoid an obvious obstruction, those that are topologically transitive contain an open and dense set. More precisely, we show that an { H}_n -extension is transitive if and only if the { R}^{2n} -extension given by the Abelianization of { H}_n is transitive. A new technical tool introduced in the paper, which is of independent interest, is a diophantine approximation result. We show, under general conditions, the existence of an infinite set of approximate positive integer solutions for a diophantine system of equations consisting of a quadratic indefinite form and several linear equations. The set of approximate solutions can be chosen to point in a certain direction. The direction can be chosen from a residual subset of full measure of the set of real directions solving the system of equations exactly. Another contribution of the paper, which is used in the proof of the main result, but it is also of independent interest, is the solution of the so-called semigroup problem for the Heisenberg group. We show that for a subset S\\subset { H}_n , which avoids any maximal semigroup with non-empty interior, the closure of the semigroup generated by S is actually a group.
NASA Astrophysics Data System (ADS)
Li, Yan-Chao; Zhu, Yuan-Hui; Yuan, Zi-Gang
2016-03-01
Using the density matrix renormalization group (DMRG) technique, we study the Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition (QPT) in the J1-J2 Heisenberg chain model from the quantum entanglement point of view. It is found that the gap behavior between two neighboring two-site entanglement entropies as well as the first derivative of both the two-site entropy and the block entropy can be used as indicators for the BKT phase transition in this model. The corresponding size dependent scaling behaviors are analyzed, respectively. Our numerical results give direct evidence for the effectiveness of the entanglement in the BKT-type QPT indicating from different aspects.
Equation of state and spin-correlation functions of ultrasmall classical Heisenberg magnets
Ciftja, O.; Luban, M.; Auslender, M.; Luscombe, J.H.
1999-10-01
We obtain analytical expressions for the total magnetic moment and the static spin-correlation functions of the classical Heisenberg model for ultrasmall systems of spins (unit vectors), that interact via isotropic, nearest-neighbor (n-n) exchange and that are subject to a uniform dc magnetic field of arbitrary strength. Explicit results are presented for the dimer, equilateral triangle, square, and regular tetrahedron arrays of spins. These systems provide a useful theoretical framework for calculating the magnetic properties of several recently synthesized molecular magnets. The tetrahedron as well as the equilateral triangle systems, each considered for n-n antiferromagnetic exchange, are of particular interest since they exhibit frustrated spin ordering for sufficiently low temperatures and weak magnetic fields. {copyright} {ital 1999} {ital The American Physical Society}
Theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet.
Brockmann, Michael; Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Weisse, Alexander
2011-07-01
We analyze the problem of microwave absorption by the Heisenberg-Ising magnet in terms of shifted moments of the imaginary part of the dynamical susceptibility. When both the Zeeman field and the wave vector of the incident microwave are parallel to the anisotropy axis, the first four moments determine the shift of the resonance frequency and the linewidth in a situation where the frequency is varied for fixed Zeeman field. For the one-dimensional model we can calculate the moments exactly. This provides exact data for the resonance shift and the linewidth at arbitrary temperatures and magnetic fields. In current ESR experiments the Zeeman field is varied for fixed frequency. We show how in this situation the moments give perturbative results for the resonance shift and for the integrated intensity at small anisotropy as well as an explicit formula connecting the linewidth with the anisotropy parameter in the high-temperature limit. PMID:21797567
Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks
NASA Astrophysics Data System (ADS)
Bogoliubov, N. M.; Malyshev, C.
2014-02-01
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Singular integral operators of near-product-type on the Heisenberg group
NASA Astrophysics Data System (ADS)
Fraser, Andrea
2007-03-01
In this paper we establish Lp-boundedness (1
Heisenberg group whose kernels satisfy regularity and cancellation conditions adapted to the implicit (n+1)-parameter structure. The polyradial kernels of this type arose in [A.J. Fraser, An (n+1)-fold Marcinkiewicz multiplier theorem on the Heisenberg group, Bull. Austral. Math. Soc. 63 (2001) 35-58; A.J. Fraser, Convolution kernels of (n+1)-fold Marcinkiewicz multipliers on the Heisenberg group, Bull. Austral. Math. Soc. 64 (2001) 353-376] as the convolution kernels of (n+1)-fold Marcinkiewicz-type spectral multipliers of the n-partial sub-Laplacians and the central derivative on the Heisenberg group. Thus they are in a natural way analogous to product-type Calderon-Zygmund convolution kernels on . Here, as in [A.J. Fraser, An (n+1)-fold Marcinkiewicz multiplier theorem on the Heisenberg group, Bull. Austral. Math. Soc. 63 (2001) 35-58; A.J. Fraser, Convolution kernels of (n+1)-fold Marcinkiewicz multipliers on the Heisenberg group, Bull. Austral. Math. Soc. 64 (2001) 353-376], we extend to the (n+1)-parameter setting the methods and results of Muller, Ricci, and Stein in [D. Muller, F. Ricci, E.M. Stein, Marcinkiewicz multipliers and two-parameter structures on Heisenberg groups I, Invent. Math. 119 (1995) 199-233] for the two-parameter setting and multipliers of the sub-Laplacian and the central derivative.
NASA Astrophysics Data System (ADS)
Qin, Meng; Zhai, Xiao-Yue; Chen, Xuan; Li, Yan-Biao; Wang, Xiao; Bai, Zhong
2012-03-01
We study the quantum discord and teleportation of a two-qubit Heisenberg XXX chain with spin-orbit interaction. The analytical expressions of quantum discord, output state quantum discord and fidelity are obtained for this model. The classical correlation, quantum correlation and entanglement of this system depending on coupling interaction, spin-orbit interaction and temperature are investigated in detail. It is found that the quantum discord exists for the ferromagnetic case, but entanglement is zero under the same condition. We can obtain fidelity better than any classical communication protocol for the antiferromagnetic case. The robustness of quantum discord against the temperature is helpful for the realization of quantum computation.
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.
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. PMID:24877919
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.
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.
Electromagnetic soliton propagation in an anisotropic Heisenberg helimagnet
NASA Astrophysics Data System (ADS)
Saravanan, M.
2014-08-01
We study the nonlinear spin dynamics of Heisenberg helimagnet under the effect of electromagnetic wave (EM) propagation. The basic dynamical equation of the spin evolution governed by Landau-Lifshitz equation resembles the director dynamics of the twist in a cholestric liquid crystal. With the use of reductive perturbation technique the perturbation is invoked for the spin magnetization and magnetic field components of the propagating electromagnetic wave. A steady-state solution is derived for the weakly nonlinear regime and for the next order, the components turn around s plane perpendicular to the propagation direction. It is found that as the electromagnetic wave propagates in the medium, both the magnetization and magnetic field modulate in the form of kink soliton modes by introducing amplitude fluctuation in the tail part of the same.
Quantum Mechanics from a Heisenberg-Type Equality
NASA Astrophysics Data System (ADS)
Hall, Michael J. W.; Reginatto, Marcel
2003-09-01
The usual Heisenberg uncertainty relation, ΔXΔP≥h¯/2, may be replaced by an exact equality for suitably chosen measures of position and momentum uncertainty, which is valid for all wave functions. This exact uncertainty relation, δXΔPnc≡h¯/2, can be generalised to other pairs of conjugate observables such as photon number and phase, and is sufficiently strong to provide the basis for moving from classical mechanics to quantum mechanics. In particular, the assumption of a nonclassical momentum fluctuation, having a strength, which scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrödinger equation.
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
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.
Adiabatic demagnetization of spin-1/2 antiferromagnetic J1-J2 Heisenberg hexagon
NASA Astrophysics Data System (ADS)
Deb, Moumita; Ghosh, Asim Kumar
2016-05-01
Analytic expressions of exact eigenvalues of the antiferromagnetic spin-1/2 J1-J2 Heisenberg hexagon in the presence of magnetic field have been obtained. Studies on the magnetization process, nature of isentrops and properties of magnetocaloric effect in terms of adiabatic demagnetization have been carried out. Magnetocaloric effect of the spin-1/2 Heisenberg hexagonal compound Cu3WO6 has been investigated with the help of these theoretical findings.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Ivanov, Nedko B.; Petrova, Svetozara I.; Schnack, Jürgen
2016-05-01
The promotion of collinear classical spin configurations as well as the enhanced tendency towards nearest-neighbor clustering of the quantum spins are typical features of the frustrating isotropic three-body exchange interactions in Heisenberg spin systems. Based on numerical density-matrix renormalization group calculations, we demonstrate that these extra interactions in the Heisenberg chain constructed from alternating S = 3/2 and σ = 1/2 site spins can generate numerous specific quantum spin states, including some partially-polarized ferrimagnetic states as well as a doubly-degenerate non-magnetic gapped phase. In the non-magnetic region of the phase diagram, the model describes a crossover between the spin-1 and spin-2 Haldane-type states.
NASA Astrophysics Data System (ADS)
Sadeghi, Azam; Alaei, Mojtaba; Shahbazi, Farhad; Gingras, Michel J. P.
2015-04-01
FeF3, with its half-filled Fe3 +3 d orbital, hence zero orbital angular momentum and S =5 /2 , is often put forward as a prototypical highly frustrated classical Heisenberg pyrochlore antiferromagnet. By employing ab initio density functional theory, we obtain an effective spin Hamiltonian for this material. This Hamiltonian contains nearest-neighbor antiferromagnetic Heisenberg, biquadratic, and Dzyaloshinskii-Moriya interactions as dominant terms and we use Monte Carlo simulations to investigate the nonzero temperature properties of this minimal model. We find that upon decreasing temperature, the system passes through a Coulomb phase, composed of short-range correlated coplanar states, before transforming into an "all-in/all-out" (AIAO) state via a very weakly first-order transition at a critical temperature Tc≈22 K, in good agreement with the experimental value for a reasonable set of Coulomb interaction U and Hund's coupling JH describing the material. Despite the transition being first order, the AIAO order parameter evolves below Tc with a power-law behavior characterized by a pseudo "critical exponent" β ≈0.18 in accord with experiment. We comment on the origin of this unusual β value.
The generalized Gibbs ensemble for Heisenberg spin chains
NASA Astrophysics Data System (ADS)
Pozsgay, Balázs
2013-07-01
We consider the generalized Gibbs ensemble (GGE) in the context of global quantum quenches in XXZ Heisenberg spin chains. Embedding the GGE into the quantum transfer matrix formalism, we develop an iterative procedure to fix the Lagrange multipliers and to calculate predictions for the long-time limit of short-range correlators. The main idea is to consider truncated GGEs with only a finite number of charges and to investigate the convergence of the numerical results as the truncation level is increased. As an example we consider a quantum quench situation where the system is initially prepared in the Néel state and then evolves with an XXZ Hamiltonian with anisotropy Δ > 1. We provide predictions for short-range correlators and gather numerical evidence that the iterative procedure indeed converges. The results show that the system retains memory of the initial condition, and there are clear differences between the numerical values of the correlators as calculated from the purely thermal and generalized Gibbs ensembles.
New Results for Heisenberg Spin Ladders Using a Plaquette Basis
NASA Astrophysics Data System (ADS)
Shepard, J. R.; Piekarewicz, J.
1997-10-01
Heisenberg spin ladders consist of interacting parallel quantum spin chains; interactions are between nearest-neighbors only. These systems are of current interest because of their rich and subtle dynamics as well as their possible relevance to high-temperature superconductors.(see, e.g.), Physics Today, October, 1996, p.17 We have formulated a novel ``plaquette basis'' for computing properties of 2-leg spin ladders. The Hamiltonian is diagonal for individual plaquettes in this basis which proves to be useful both calculationally and for providing a physical picture of the dynamics of the ladders. Implementation of this basis requires Racah algebra techniques familiar in nuclear and atomic physics but relatively unknown in condensed matter physics. We present plaquette-basis calculations for various properties of 2-leg ladders with up to 8 rungs. For the larger ladders, we use COntractor REnormalization (CORE(C.J. Morningstar and M. Weinstein, hep-lat)/9603016) methods to correct for truncations. We also present a Renormalization Group scheme which permits us to treat arbitrarily large ladders. Comparisons to and extensions of previous calculations will be presented.
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.
NASA Astrophysics Data System (ADS)
Körpinar, Talat; Asi˙l, Vedat; Turhan, Essin
2015-01-01
In this paper, we obtain the new parametric representation for a time-involute particles in Heisenberg spacetime . By using the Frenet frame, we derive the necessary and sufficient conditions to construct a biharmonic particle Heisenberg spacetime . We give a geometrical description of time-involute particles around timelike biharmonic particle in . Moreover, we obtain Lorentz transformations this particles. Finally, we give the relationship of electromagnetic fields on Heisenberg spacetime.
Boggy, R.; Franz, F.A.
1982-04-01
We have used selective excitation and monitoring of individual (J,m/sub J/) Zeeman sublevels of the 4 /sup 2/P/sub 1/2/ and 4 /sup 2/P/sub 3/2/ states of K at 22 kG and 131 kG to measure (J,m/sub J/..-->..J', m/sub J/') transition cross sections for K colliding with He, Ne, and Kr at 380 K. The results, translated into irreducible tensor cross sections for depolarization are, in units of 10/sup -16/ cm/sup 2/: /sup 2/P/sub 3/2/; ..lambda../sup 1//sub 3/2/(He) = 97 +- 13; ..lambda../sup 2//sub 3/2/(He) = 130 +- 17; ..lambda../sup 3//sub 3/2/(He) = 99 +- 23 ..lambda../sup 1//sub 3/2/(Ne) = 103 +- 10; ..lambda../sup 2//sub 3/2/(Ne) = 146 +- 14; ..lambda../sup 3//sub 3/2/ (Ne) = 111 +- 14 ..lambda../sup 1//sub 3/2/(Kr) = 270 +- 24; ..lambda../sup 2//sub 3/2/(Kr) = 341 +- 29; ..lambda../sup 3//sub 3/2/(Kr) = 276 +- 30 /sup 2/P/sub 1/2/; ..lambda../sup 1//sub 1/2/(He) = 45 +- 5 ..lambda../sup 1//sub 1/2/(Ne) = 56 +- 6 ..lambda../sup 1//sub 1/2/(Kr) = 81 +- 6. The measured total cross sections for intramultiplet transitions, sigma/sup 0//sub 1/2/(/sup 2/P/sub 1/2/..-->../sup 2/P/sub 3/2/) and sigma/sup 0//sub 3/2/ (/sup 2/P/sub 3/2/..-->.. /sup 2/P/sub 1/2/), are, in units of 10/sup -16/ cm/sup 2/: sigma/sup 0//sub 1/2/(He) = 36.5 +- 9.5; sigma/sup 0//sub 3/2/(He) = 18.7 +- 7 sigma/sup 0//sub 3/2/(Ne) = 5.9 +- 2.6 sigma/sup 0//sub 3/2/(Kr) = 25 +- 7
Quantum phase transitions in triangular lattice Heisenberg anti-ferromagnet in a magnetic field
NASA Astrophysics Data System (ADS)
Ye, Mengxing; Chubukov, Andrey
We present the zero temperature phase diagram of a large S Heisenberg anti-ferromagnet on a frustrated triangular lattice with the nearest neighbor (J1) and the next nearest neighbor (J2) interactions, in a magnetic field. We show that the classical model has an ``accidental'' degeneracy for all J2 /J1 and all fields below the saturation field, which gives rise to the extended manifold of the ground state spin configurations. Quantum fluctuations, however, lift this degeneracy. For small J2 /J1 , they select one of three different co-planar states, depending on the field value. We argue that above some critical ratio of J2 /J1 , which weakly depends on a magnetic field, these fluctuations select the stripe phase. We analyze in detail the mechanism of the selection of the stripe phase and explore the nature of the quantum phase transition in a magnetic field between the ordered phases as J2 /J1 passes through a critical value.
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.
NASA Astrophysics Data System (ADS)
Petersen, Jakob; Pollak, Eli
2015-12-01
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.
NASA Astrophysics Data System (ADS)
Yamaguchi, H.; Okubo, T.; Iwase, K.; Ono, T.; Kono, Y.; Kittaka, S.; Sakakibara, T.; Matsuo, A.; Kindo, K.; Hosokoshi, Y.
2013-11-01
We have succeeded in synthesizing single crystals of the verdazyl radical β-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl. The ab initio molecular orbital calculation indicates the formation of an S=1/2 Heisenberg antiferromagnetic chain with fourfold magnetic periodicity consisting of three types of exchange interactions. We successfully explain the magnetic and thermodynamic properties based on the expected spin model by using the quantum Monte Carlo method. Furthermore, we reveal that the alternating and unique Ising ferromagnetic chains become effective in the specific field regions and observe a cooperative phenomenon caused by the magnetic order and quantum fluctuations. These results demonstrate that the verdazyl radical could form an unconventional spin model with interesting quantum behavior and provide a way to study a variety of quantum spin systems.
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
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.
A Heisenberg Algebra Bundle of a Vector Field in Three-Space and its Weyl Quantization
Binz, Ernst; Pods, Sonja
2006-01-04
In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group H{sub X}{sup {infinity}}. A representation of the C*-group algebra of H{sub X}{sup {infinity}} is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.
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.
Lombardini, Richard; Poirier, Bill
2006-09-01
A particular basis set method developed by one of the authors, involving maximally localized orthogonal Weyl-Heisenberg wavelets (or "weylets") and a phase space truncation scheme, has been successfully applied to exact quantum calculations for many degrees of freedom (DOF's) [B. Poirier and A. Salam, J. Chem. Phys. 121, 1740 (2004)]. However, limitations in accuracy arise in the many-DOF case, owing to memory limits on conventional computers. This paper addresses this accuracy limitation by introducing phase space region operators (PSRO's) that customize individual weylet basis functions for the problem of interest. The construction of the PSRO's is straightforward, and does not require a priori knowledge of the desired eigenstates. The PSRO, when applied to weylets, as well as to simple phase space Gaussian basis functions, exhibits remarkable improvements in accuracy, reducing computed eigenvalue errors by orders of magnitude. The method is applied to various model systems at varying DOF's. PMID:17025784
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)
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.
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)
Dhar, Abhishek; Sriram Shastry, B.
2000-09-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1D for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. They are identified as generalized quantum Bloch wall states, and a simple physical picture is provided for the same.
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.
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.
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…
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.
Permutation-parity exchange at a beam splitter: Application to Heisenberg-limited interferometry
Campos, Richard A.; Gerry, Christopher C.
2005-12-15
Quantum-optical permutation and parity observables are unitarily exchanged by a 50:50 beam splitter. Bosonic coalescence effects are reexamined from this point of view. We show that photon-number resolving counters behind a beam splitter define a permutation detector for the input optical field. With suitable phase encoding, the detector also enables Heisenberg-limited interferometry.
a Path-Integration Approach to the Correlators of XY Heisenberg Magnet and Random Walks
NASA Astrophysics Data System (ADS)
Bogoliubov, N. M.; Malyshev, C.
2008-11-01
The path integral approach is used for the calculation of the correlation functions of the XY Heisenberg chain. The obtained answers for the two-point correlators of the XX magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.
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.
Thermal entanglement of the Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya interaction
NASA Astrophysics Data System (ADS)
Qiao, Jie; Zhou, Bin
2015-11-01
We investigate the thermal entanglement in a spin-1/2 Ising-Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii-Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including Dz and Dx, on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters (Dz and Dx) have remarkably different influences on the entanglement. Different from the case Dz, there is the non-monotonic variation of the concurrence with temperature in the case Dx, and additionally the DM interaction Dx can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case Dx is larger than that of the case Dz. Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
Local Magnetization in the Impure Spin 1/2 Anisotropic Ising-Heisenberg Chains
NASA Astrophysics Data System (ADS)
Gildenblat, Gennady
A theory of the Friedel-type oscillations of the local magnetization in the impure antiferromagnetic spin 1/2 chains is developed using the Green function equations of motion in the pseudo-fermion representation. For the isotropic XY (XX) chain, the problem is solved exactly, while the Ising-Heisenberg model is investigated numerically within a temperature-dependent Hartree-Fock approximation. It is shown that the Hartree-Fock self consistency equations for the uniformly magnetized XXZ chain can be recovered as a particular case of the formalism developed in the present work. Comparison with the earlier perturbation theory treatment in a free-fermion approximation reveals that the magnetic field dependence of the perturbation of the local magnetization is sensitive to the formation of the localized states and the exact form of the energy dispersion law of the quasi-particles. In particular it is shown that the perturbations of the local magnetization in the impure spin 1/2 chains disappear in the absence of the external magnetic field. Using the exact solution for the XY chain it is shown that unless the localized energy levels are formed outside the pseudo-fermion energy band the singularity of the local magnetization existing in the pure chain disappears at an arbitrary distance from the single impurity spin. For the ferromagnetic chain with the ferromagnetically coupled impurity the solution of the Hartree-Fock equations at low temperatures agrees reasonably with the results of the linear spin-wave theory. If the impurity is antiferromagnetically coupled, then, in contrast with the results of the spin -wave theory, the Hartree-Fock approximation agrees with the exact result for the zero-field ground state spin defect at the impurity site. Unlike the previous methods, the technique developed in this work permits investigation of the whole temperature range and predicts the correct Curie-Weiss behavior at sufficiently large temperatures.
NASA Astrophysics Data System (ADS)
Mazurova, Elena; Lapshin, Aleksey
2013-04-01
precisely, what frequency is present in the signal at the current moment of time: it is possible to speak only about the range of frequencies. Besides, it is impossible to specify precisely the time moment of the presence of this or that frequency: it is possible to speak only about the time frame. It is this feature that imposes major constrains on the applicability of the STFT. In spite of the fact that the problems of resolution in time and frequency result from a physical phenomenon (Heisenberg's uncertainty principle) and exist independent of the transform applied, there is a possibility to analyze any signal, using the alternative approach - the multiresolutional analysis (MRA). The wavelet-transform is one of the methods for making a MRA-type analysis. Thanks to it, low frequencies can be shown in a more detailed form with respect to time, and high ones - with respect to frequency. The paper presents the results of calculating of the components of the deflection of the vertical, done by the SFT, STFT and WT. The results are presented in the form of 3-d models that visually show the action of Heisenberg's uncertainty principle in the specified algorithms. The research conducted allows us to recommend the application of wavelet-transform to calculate of the components of the deflection of the vertical in the near-field zone. Keywords: Standard Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, Heisenberg's uncertainty principle.
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.
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.
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
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
NASA Astrophysics Data System (ADS)
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 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 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.
Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements
Campos, R. A.; Gerry, Christopher C.; Benmoussa, A.
2003-08-01
Holland and Burnett [Phys. Rev. Lett. 71, 1355 (1993)] have argued that twin Fock states of equal photon number N injected at both input ports of a Mach-Zehnder interferometer lead to phase measurements with accuracies approaching the Heisenberg limit {delta}{phi}{sub HL}=1/(2N). However, the method of phase detection suggested by those authors, obtaining the difference of the photocurrents at the output ports of the interferometer, is not sensitive to the phase difference between the two interferometer paths; in fact, the photocurrent vanishes. In this paper we show that the use of parity measurements on just one of the output modes not only is sensitive to the phase difference but that the sensitivity approaches the Heisenberg limit for large N.
Representation of the Heisenberg Algebra h4 by the Lowest Landau Levels and Their Coherent States
NASA Astrophysics Data System (ADS)
Fakhri, H.; Shadman, Z.
Using simultaneous shape invariance with respect to two different parameters, we introduce a pair of appropriate operators which realize shape invariance symmetry for the monomials on a half-axis. It leads to the derivation of rotational symmetry and dynamical symmetry group H4 with infinite-fold degeneracy for the lowest Landau levels. This allows us to represent the Heisenberg-Lie algebra h4 not only by the lowest Landau levels, but also by their corresponding standard coherent states.
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
Algebraic Bethe ansatz for Q-operators: the Heisenberg spin chain
NASA Astrophysics Data System (ADS)
Frassek, Rouven
2015-07-01
We diagonalize Q-operators for rational homogeneous {sl}(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxter's Q-functions.
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).
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.-/
Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number s ≥ 1
NASA Astrophysics Data System (ADS)
Li, P. H. Y.; Bishop, R. F.; Campbell, C. E.
2016-03-01
The ground-state (GS) phase diagram of the frustrated spin-s J1-J2-J3 Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method implemented to high orders of approximation, for spin quantum numbers s = 1, 3/2, 2 , 5/2. The model has antiferromagnetic (AFM) nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour exchange couplings (with strength J1 > 0, J2 > 0 and J3 > 0, respectively). We specifically study the case J3 = J2 = κJ1, in the range 0 < κ < 1 of the frustration parameter, which includes the point of maximum classical (s → ∞) frustration, viz., the classical critical point at κcl = 1/2, which separates the Neel phase for κ < κcl and the collinear striped AFM phase for κ > κ cl. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins s > 3/2 we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value κc(s) which is slightly greater than κcl [e.g., κc(3/2) ≈ 0.53(1)] and which approaches it monotonically as s → ∞. By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Néel AFM order for κ < κc1 = 0.485(5) and one with striped AFM order for κ > κc2 = 0.528(5), just as in the case s = 1/2 (for which κc1 ≈ 0.47 and κc2 ≈ 0.60). For both the s = 1/2 and s = 1 models the transition at κc2 appears to be of first-order type, while that at κc1 appears to be continuous. However, whereas in the s = 1/2 case the intermediate phase appears to have PVBC order over the entire range κc1 < κ < κc2, in the s = 1 case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.
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)
Shinaoka, Hiroshi; Tomita, Yusuke; Motome, Yukitoshi
2014-10-01
Motivated by puzzling aspects of spin-glass behavior reported in frustrated magnetic materials, we theoretically investigate effects of magnetoelastic coupling in geometrically frustrated classical spin models. In particular, we consider bond-disordered Heisenberg antiferromagnets on a pyrochlore lattice coupled to local lattice distortions. By integrating out the lattice degree of freedom, we derive an effective spin-only model, the bilinear-biquadratic model with bond disorder. The effective model is analyzed by classical Monte Carlo simulations using an extended loop algorithm. First, we discuss the phase diagrams in detail by showing the comprehensive Monte Carlo data for thermodynamic and magnetic properties. We show that the spin-glass transition temperature Tf is largely enhanced by the spin-lattice coupling b in the weakly disordered regime. By considering the limit of strong spin-lattice coupling, this enhancement is ascribed to the suppression of thermal fluctuations in semidiscrete degenerate manifold formed in the presence of the spin-lattice coupling. We also find that, by increasing the strength of disorder Δ, the system shows a concomitant transition of the nematic order and spin glass at a temperature determined by b, being almost independent of Δ. This is due to the fact that the spin-glass transition is triggered by the spin collinearity developed by the nematic order. Although further-neighbor exchange interactions originating in the cooperative lattice distortions result in spin-lattice order in the weakly disordered regime, the concomitant transition remains robust with Tf almost independent of Δ. We find that the magnetic susceptibility shows hysteresis between the field-cooled and zero-field-cooled data below Tf, and that the nonlinear susceptibility shows a negative divergence at the transition. These features are common to conventional spin-glass systems. Meanwhile, we find that the specific heat exhibits a broad peak at Tf, and that the
Field-induced quantum criticality in low-dimensional Heisenberg spin systems
NASA Astrophysics Data System (ADS)
Azzouz, Mohamed
2006-11-01
We study the quantum critical behavior in the antiferromagnetic Heisenberg chain and two-leg Heisenberg ladder resulting from the application of an external magnetic field. In each of these systems a finite-temperature crossover line between two different ferromagnetic phases ends with a quantum critical point at zero temperature. Using the bond-mean-field theory, we calculate the field dependence of the magnetization and the mean-field spin bond parameters in both systems. For the Heisenberg chain, we recover the existing exact results and show in addition that the saturation of the zero-temperature magnetization at the field hc=2J is accompanied by a quantum phase transition, where the bond parameter vanishes. Here J is the exchange coupling constant along the chain. For the two-leg ladder, we also recover the known results, like the two magnetization plateaus, and show that at the upper critical field, which corresponds to the appearance of the saturation magnetization plateau, the chain and rung spin bond parameters vanish. The identification of the order parameters that govern the field-induced quantum criticality in the systems we study here constitutes an original contribution. Because no long-range order, which breaks symmetry, characterizes the bond order, the latter could be a proposal for the so-called hidden order. We calculate analytically the bond parameters in both systems as functions of the field in the low- and high-field limits at zero temperature. At nonzero temperatures, the calculation of the magnetization and bond parameters is carried out by solving the mean-field equations numerically.
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.
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.
Heisenberg-limited quantum sensing and metrology with superpositions of twin-Fock states
NASA Astrophysics Data System (ADS)
Gerry, Christopher C.; Mimih, Jihane
2011-03-01
We discuss the prospects of performing Heisenberg-limited quantum sensing and metrology using a Mach-Zehnder interferometer with input states that are superpositions of twin-Fock states and where photon number parity measurements are made on one of the output beams of the interferometer. This study is motivated by the experimental challenge of producing twin-Fock states on opposite sides of a beam splitter. We focus on the use of the so-called pair coherent states for this purpose and discuss a possible mechanism for generating them. We also discuss the prospect of using other superstitions of twin-Fock states, for the purpose of interferometry.
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. PMID:24394808
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.
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.
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
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
NASA Astrophysics Data System (ADS)
Gong, Jia-Min; Tang, Qi; Sun, Yu-Hang; Qiao, Lin
2015-03-01
We studied the trace distance, the Hellinger distance, and the Bures distance geometric quantum discords (GQDs) for a two-spin Heisenberg XX chain with the Dzyaloshinsky-Moriya (DM) interaction and the external magnetic fields. We found that considerable enhancement of the GQDs can be achieved by introducing the DM interaction, and their maxima were obtained when the strength of the DM interaction approaches infinity. The external magnetic fields and the increase of the temperature can also enhance the GQDs to some extent during certain specific parameter regions.
Scriven, E P; Powell, B J
2012-08-31
We show that the electronic structures of the title compounds predicted by density functional theory are well described by tight binding models. We determine the frustration ratio, J'/J, of the Heisenberg model on the anisotropic triangular lattice, which describes the spin degrees of freedom in the Mott insulating phase for a range of Pd(dmit)2 salts. All of the antiferromagnetic materials studied have J'/J is < or approximately equal to 0.5 or J'/J > or approximately equal to 0.9, and all salts with 0.5 < or approximately equal to J'/J < or approximately equal to 0.9 are known, experimentally, to be charge ordered valence-bond solids or spin liquids. PMID:23002879
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.
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.
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.
NASA Astrophysics Data System (ADS)
Castro, Carlos
2006-11-01
A novel Weyl-Heisenberg algebra in Clifford spaces is constructed that is based on a matrix-valued {\\cal H}^{AB} extension of Planck's constant. As a result of this modified Weyl-Heisenberg algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px), (x, py), (x, pz), (y, px), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's noncommutative spacetime algebra and the area-coordinates algebra associated with Clifford spaces. The former Yang's algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = planck/R (maximal length R, infrared cutoff). The double-scaling limit of Yang's algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L2 = nλ2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n. It is shown how modified Newtonian dynamics is also a consequence of Yang's algebra resulting from the modified Poisson brackets. Finally, another noncommutative algebra which differs from Yang's algebra and related to the minimal length uncertainty relations is presented. We conclude with a discussion of the implications of noncommutative QM and QFT's in Clifford spaces.
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.
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.
J=0,J=J{sub max}, and quadrupole pairing
Hertz-Kintish, Daniel; Zamick, Larry
2014-12-15
We consider 2 neutrons and 2 protons in the g{sub 9/2} shell. Wave functions and energy levels are obtained for various interactions. The wavefunctions for states with total angular momentum I greater than or equal to 10 are not affected by what the pairing interaction (J=0T=1) is. Other parts of the interaction are therefore of increased importance. Furthermore, states with I greater than or equal to 12 are not affected by the J=2 interaction.
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.
Microscope and spectroscope results are not limited by Heisenberg's Uncertainty Principle!
NASA Astrophysics Data System (ADS)
Prasad, Narasimha S.; Roychoudhuri, Chandrasekhar
2011-09-01
A reviewing of many published experimental and theoretical papers demonstrate that the resolving powers of microscopes, spectroscopes and telescopes can be enhanced by orders of magnitude better than old classical limits by various advanced techniques including de-convolution of the CW-response function of these instruments. Heisenberg's original analogy of limited resolution of a microscope, to support his mathematical uncertainty relation, is no longer justifiable today. Modern techniques of detecting single isolated atoms through fluorescence also over-ride this generalized uncertainty principle. Various nano-technology techniques are also making atoms observable and location precisely measurable. Even the traditional time-frequency uncertainty relation or bandwidth limit δvδt >= 1 can be circumvented while doing spectrometry with short pulses by deriving and de-convolving the pulse-response function of the spectrometer just as we do for CW input.
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.
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).
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.
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.
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.
Quantum discord in spin-1/2 Heisenberg chains with Dzyaloshinkii-Moriya interaction
NASA Astrophysics Data System (ADS)
Ma, Xiao San; Wang, An Min
2015-12-01
We have investigated the quantum discord (QD) of the thermal density matrix of spin-1/2 Heisenberg chains with Dzyaloshinskii-Moriya (DM) interaction. With fermionization technique, we study the mutual effect of DM interaction and the external magnetic field on the QD and the entanglement. Our analysis implies that the DM interaction can enhance the QD while the external magnetic field will shrink the QD. By a comparison between the entanglement and the QD, we find that the QD is more robust to the temperature and to the external magnetic field than the entanglement of formation (EoF) in the sense that the EoF takes a zero value while the QD does not for high temperature and strong external magnetic field. This point confirms the conclusion that there exist some separable states containing non-zero QD.
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
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.
Beyond Unitary Parasupersymmetry from the Viewpoint of h3 and h4 Heisenberg Algebras
NASA Astrophysics Data System (ADS)
Chenaghlou, A.; Fakhri, H.
Using the partition of the number p-1 into p-1 real parts which are not equal with each other necessarily, we develop the unitary parasupersymmetry algebra of arbitrary order p so that the well-known Rubakov-Spiridonov-Khare parasupersymmetry becomes a special case of the developed one. It is shown that the developed algebra is realized by simple harmonic oscillator and Landau problem on a flat surface with the symmetries of h3 and h4 Heisenberg-Lie algebras. For this new parasupersymmetry, the well-known unitary condition is violated, however, unitarity of the corresponding algebra is structurally conserved. Moreover, the components of the bosonic Hamiltonian operator are derived as functions from the mean value of the partition numbers with their label weight function.
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
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
NASA Astrophysics Data System (ADS)
Rahmani, Armin
2015-10-01
Based on the Heisenberg-picture analog of the master equation, we develop a method for computing the exact time dependence of noise-averaged observables for general noninteracting fermionic systems with noisy fluctuations. Upon noise averaging, these fluctuations generate effective interactions, limiting analytical approaches. While the short-time dynamics can be studied with Langevin-type numerical simulations, the long-time limit is not amenable to such simulations. Our results provide access to this long-time limit. As a simple example, we examine the fate of the fractional charge in cold-atom emulations of polyacetylene after stochastic driving. We find that in a quantum quench to a fluctuating hopping Hamiltonian, the fractional charge remains robust for hopping between different sublattices, while it becomes unstable in the presence of noisy hopping on the same sublattice.
Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain
NASA Astrophysics Data System (ADS)
Lajkó, Péter; Carlon, Enrico; Rieger, Heiko; Iglói, Ferenc
2005-09-01
We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, z , and z=1 signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.
NASA Astrophysics Data System (ADS)
Mi, Bin-Zhou; Zhai, Liang-Jun; Hua, Ling-Ling
2016-01-01
The effect of magnetic spin correlation on the thermodynamic properties of Heisenberg ferromagnetic single-walled nanotubes are comprehensively investigated by use of the double-time Green's function method. The influence of temperature, spin quantum number, diameter of the tube, anisotropy strength and external magnetic field to internal energy, free energy, and magnon specific heat are carefully calculated. Compared to the mean field approximation, the consideration of the magnetic correlation effect significantly improves the internal energy values at finite temperature, while it does not so near zero temperature, and this effect is related to the diameter of the tube, anisotropy strength, and spin quantum number. The magnetic correlation effect lowers the internal energy at finite temperature. As a natural consequence of the reduction of the internal energy, the specific heat is reduced, and the free energy is elevated.
Bagchi, Debarshee
2013-12-11
Using computer simulation we investigate thermal transport in a two segment classical Heisenberg spin chain with nearest neighbor interaction and in the presence of an external magnetic field. The system is thermally driven by heat baths attached at the two ends and transport properties are studied using energy conserving dynamics. We demonstrate that by properly tuning the parameters thermal rectification can be achieved-the system behaves as a good conductor of heat along one direction but becomes a bad conductor when the thermal gradient is reversed, and crucially depends on nonlinearity and spatial asymmetry. Moreover, suitable tuning of the system parameters gives rise to the counterintuitive and technologically important feature known as negative differential thermal resistance (NDTR). We find that the crucial factor responsible for the emergence of NDTR is a suitable mechanism for impeding the current in the bulk of the system. PMID:24195913
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.
Anomalous Curie Response of Impurities in Quantum-Critical Spin-1/2 Heisenberg Antiferromagnets
NASA Astrophysics Data System (ADS)
Höglund, Kaj H.; Sandvik, Anders W.
2007-07-01
We consider a magnetic impurity in two different S=1/2 Heisenberg bilayer antiferromagnets at their respective critical interlayer couplings separating Néel and disordered ground states. We calculate the impurity susceptibility using a quantum Monte Carlo method. With intralayer couplings in only one of the layers (Kondo lattice), we observe an anomalous Curie constant C*, as predicted on the basis of field-theoretical work [S. Sachdev , Science 286, 2479 (1999)SCIEAS0036-807510.1126/science.286.5449.2479]. The value C*=0.262±0.002 is larger than the normal Curie constant C=S(S+1)/3. Our low-temperature results for a symmetric bilayer are consistent with a universal C*.
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.
NASA Astrophysics Data System (ADS)
Uys, Hermann
Cooperative effects in many-particle systems can be exploited to achieve measurement outcomes not possible with independent probe particles. We explore two measurement applications based on the cooperative phenomenon of superradiance or on correlated quantum states closely related to superradiance. In the first application we study the off-resonant superradiant Raman scattering of light from an ultracold Bose atomic vapor. We investigate the temperature dependence of superradiance for a trapped vapor and show that in the regime where superradiance occurs on a timescale comparable to a trap frequency, scattering takes place preferentially from atoms in the lowest trap levels due to Doppler dephasing. As a consequence, below the critical temperature for Bose condensation, absorption images of transmitted light serve as a direct probe of the condensed state. Subsequently, we consider a pure condensate and study the time-dependent spatial features of transmitted light, obtaining good qualitative agreement with recent imaging experiments. Inclusion of quantum fluctuations in the initial stages of the superradiant emission accounts well for shot-to-shot fluctuations. Secondly, we have used simulated annealing, a global optimization strategy, to systematically search for correlated quantum interferometer input states that approach the Heisenberg limited uncertainty in estimates of the interferometer phase shift. That limit improves over the standard quantum limit to the phase sensitivity of interferometric measurements by a factor of 1/ N , where N is the number of interfering particles. We compare the performance of these states to that of other non-classical states already known to yield Heisenberg limited uncertainty.
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.
The Hydrogen Atom: The Rutherford Model
NASA Astrophysics Data System (ADS)
Tilton, Homer Benjamin
1996-06-01
Early this century Ernest Rutherford established the nuclear model of the hydrogen atom, presently taught as representing the best visual model after modification by Niels Bohr and Arnold Sommerfeld. It replaced the so-called "plum pudding" model of J. J. Thomson which held sway previously. While the Rutherford model represented a large step forward in our understanding of the hydrogen atom, questions remained, and still do.
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
Gerry, Christopher C.; Campos, R. A.
2003-08-01
We outline a procedure for Heisenberg-limited phase resolution between two Bose-Einstien condensates (BECs) defined as different hyperfine levels. The method involves first establishing a maximally entangled state using the ideas of nonlinear interferometry previously discussed in the optical domain [C. C. Gerry et al., Phys. Rev. A 66, 013804 (2002)]. In the case of the condensates, the nonlinear interactions are realized by the interatomic interactions within each condensate. Quarter cycle Raman pulses between hyperfine levels act as beam splitters. Parity measurements of one of the components of the BEC resolve the phase at the Heisenberg limit. We point out that parity measurements can be made by coupling the mode of interest with a third condensate where both components evolve under nonlinear interatomic interactions. After another Raman pulse, the components are populated according to parity. One need only determine which component is populated to determine the parity.
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
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.
Heat Conductivity of the Heisenberg Spin-1 /2 Ladder: From Weak to Strong Breaking of Integrability
NASA Astrophysics Data System (ADS)
Steinigeweg, Robin; Herbrych, Jacek; Zotos, Xenophon; Brenig, Wolfram
2016-01-01
We investigate the heat conductivity κ of the Heisenberg spin-1 /2 ladder at finite temperature covering the entire range of interchain coupling J⊥, by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction κ ∝J⊥-2 , based on simple golden-rule arguments and valid in the strict limit J⊥→0 , applies to a remarkably wide range of J⊥, qualitatively and quantitatively. In the large J⊥ limit, we show power-law scaling of opposite nature, namely, κ ∝J⊥2. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at J⊥=J∥. Reducing temperature T , starting from T =∞ , this minimum scales as κ ∝T-2 down to T on the order of the exchange coupling constant. These results provide for a comprehensive picture of κ (J⊥,T ) of spin ladders.
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.
The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains.
Fertitta, Edoardo; El Khatib, Muammar; Bendazzoli, Gian Luigi; Paulus, Beate; 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 Sz has been derived. PMID:26723672
Optimal transport and von Neumann entropy in a Heisenberg XXZ chain out of equilibrium.
Salerno, Mario; Popkov, Vladislav
2013-02-01
In this paper we investigate the spin currents and the von Neumann entropy (vNE) of a Heisenberg XXZ chain in contact with twisted XY-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the vNE. As a result we show that the maximal spin current always occurs in the proximity of minima of the vNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. As the coupling is increased, current reversals may occur and in the limit of strong coupling we show that minima of the vNE tend to zero, meaning that the maximal transport is achieved in this case with states that are very close to pure states. PMID:23496461
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. PMID:21474883
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.
Modification of the classical Heisenberg helimagnet by weak uniaxial anisotropy and magnetic field
Zaliznyak, I.A.; Zhitomirsky, M.E.
1995-09-01
A classical ground state of the isotropic Heisenberg spin Hamiltonian on a primitive Bravais lattice is known to be a single-Q plane helix. Additional uniaxial anisotropy and external magnetic field can greatly distort this structure by generating higher-order (at the wave vectors nQ) Fourier harmonics in the spatial spin configuration. These features are not captured within the usual formalism based on the Luttinger-Tisza theorem, when the classical ground state energy is minimized under the {open_quotes}weak{close_quotes} condition on the lengths of the spins. We discuss why the correct solution is lost in that approach and present another microscopic treatment of the problem. For easy-axis and easy-plane quadratic uniaxial anisotropy it allows one to find the classical ground state for general Q and for any orientation of the magnetic field considering the effect of anisotropy (but not the field) as a perturbation of the exchange structure. As a result, the classical ground state energy, the uniform magnetization, and the magnetic Bragg peak intensities that are measured in the experiments are calculated. 21 refs., 1 fig.
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 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.
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.
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.
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.
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.
Anomalous Curie response of an impurity in a quantum critical spin-1/2 Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Höglund, Kaj; Sandvik, Anders
2007-03-01
There is a disagreement concerning the low-temperature (T) magnetic susceptibility χ^zimp˜C/T of a spin-S impurity in a nearly quantum critical antiferromagnetic host. Field-theoretical work [1] predicted an anomalous Curie constant S^2/3
Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model
NASA Astrophysics Data System (ADS)
Burić, Maja; Madore, John; Nenadović, Luka
2015-09-01
We analyse the Dirac action on the truncated Heisenberg algebra and in particular, the nonminimal couplings to the background gravitational field. By projection to the Heisenberg algebra we obtain a renormalisable model: the noncommutative extension of the Gross-Neveu model. This result indicates that, as on the commutative curved backgrounds, nonminimal couplings with torsion and curvature are necessary (and sufficient) for renormalisability of scalar and spinor theories on the curved noncommutative spaces.
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
Neutron Scattering Study of the S=1/2 Heisenberg AFM Chain Cu(C_6D_5COO)2 \\cdot 3D_2O
NASA Astrophysics Data System (ADS)
Dender, D. C.; Reich, D. H.; Broholm, C.; Lefmann, K.; Aeppli, G.
1996-03-01
Quasi-one-dimensional magnetic materials provide the opportunity to test rigorously models of simple, interacting many-body systems. We present triple-axis neutron scattering measurements of the temperature and magnetic field dependence of spin correlations in the quasi-1D S=1/2 Heisenberg antiferromagnet Cu(C_6D_5COO)2 \\cdot3D_2O. We have measured the temperature evolution of the spin-spin correlation length κ over the temperature range 0.1J < k_BT < 0.8J, where J is the nearest-neighbor coupling strength. Measurements of S^zz(q = π , ω , T) are found to be described by a finite temperature field theory.(H. J. Schulz, Phys. Rev. B 34), 6372 (1986). At high magnetic fields, new features are observed close to q=π consistent with predictions of non-classical behavior.(N. Ishimura and H. Shiba, Prog. Theor. Phys. Jpn. 57), 1862 (1977).^,(G. Müller, H. Thomas, H. Beck, and J. C. Bonner, Phys. Rev. B 24), 1429 (1981). ^*supported by NSF Grants DMR93-02065 and DMR94-53362, and by the David and Lucile Packard Foundation.
NASA Astrophysics Data System (ADS)
Becca, Federico; Iqbal, Yasir; Poilblanc, Didier
2012-02-01
Within the class of Gutzwiller projected fermionic wave functions, by using quantum variational Monte Carlo simulations, we investigated the energetics of all possible Z2 spin liquids that can potentially occur as ground states of the nearest-neighbor S=1/2 quantum Heisenberg model on the Kagome lattice [1]. We conclusively show that all gapped and gapless Z2 spin liquids are higher in energy compared to the U(1) gapless states in whose neighborhoods they lie. In particular, the most promising gapped Z2 spin liquid (the so-called Z2[0,π]β state), conjectured to describe the ground state [2], is always higher in energy compared to the U(1) Dirac spin liquid. We also extended the U(1) Dirac state and the uniform RVB spin liquid to include next-nearest-neighbor hopping terms, and studied its local and global stability towards various valence bond crystal patterns. We found that a non-trivial 36-site VBC is stabilized upon addition of a small ferromagnetic exchange coupling [3]. [4pt] [1] Y. Iqbal, F. Becca, and D. Poilblanc, Phys. Rev. B 84, 020407(R) (2011)[0pt] [2] Y.-M. Lu, Y. Ran, and P.A. Lee. Phys. Rev. B 83, 224413 (2011)[0pt] [3] Y. Iqbal, F. Becca, and D. Poilblanc, Phys. Rev. B 83, 100404(R) (2011)
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
NASA Astrophysics Data System (ADS)
Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang
2015-04-01
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.
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.
Maeter, H; Zvyagin, A A; Luetkens, H; Pascua, G; Shermadini, Z; Saint-Martin, R; Revcolevschi, A; Hess, C; Büchner, B; Klauss, H-H
2013-09-11
We report zero and longitudinal magnetic field muon spin relaxation (μSR) measurements of the spin S = 1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B0 the spin-lattice relaxation rate λ follows a power law λ is proportional to B(0)(-n) with n = 0.9(3). This result is temperature independent for 5 K ≤ T ≤ 300 K. Within conformal field theory and using the Müller ansatz we conclude ballistic spin transport in SrCuO2. PMID:23924574
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)
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.
Entanglement in the Majumdar-Ghosh model
Chhajlany, Ravindra W.; Tomczak, Piotr; Wojcik, Antoni; Richter, Johannes
2007-03-15
We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or J{sub 1}-J{sub 2} Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behavior of the entanglement entropy characterizing the unfrustrated Heisenberg chain above J{sub 2}{approx_equal}0.25. This feature can be used as an indicator of the dimer phase transition occurring in this model. Additionally, we also consider entanglement at the MG point J{sub 2}=0.5J{sub 1}.
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)
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
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…
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…
NASA Astrophysics Data System (ADS)
Li, B.; Palmans, H.; Hao, L.; Nisbet, A.
2015-09-01
As the wavelengths of low energy electrons become comparable with the length scale of the mean ionisation step size, each event particle should be treated with care as the condition outlined in Heisenberg's uncertainty principle (HUP) should also be satisfied. Within this quantum-classical regime, spatial delocalisations of individual ionisation event sites that are generated outside the target region are calculated, and particular attention is given to the validity of using classical transport methods in simulations of nanodosimetric parameters such as mean cluster size, first and second moments, variance and cumulative frequency of ionisation cluster-size probability distributions. This paper presents the comparison between conventionally calculated nanodosimetric quantities and the ones where interacting particles are treated semi-classically with spatial uncertainties satisfied by HUP. The simulated primary charged particles are electrons of energies between 100 eV and 1 keV in DNA equivalent target aqueous water volumes using GEANT4-DNA.
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.
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 flop relaxation in the quasi-1d Heisenberg antiferromagnet CsMnBr 3 · 2H 2O
NASA Astrophysics Data System (ADS)
Chirwa, M.; Top, J.; Flokstra, J.
1983-12-01
The relaxation phenomena associated with the antiferromagnetic to spin-flop phase transition in the quasi one dimensional Heisenberg antiferromagnet CsMnBr 3 · 2H 2O have been determined in the temperature range 1.6-4.2 K using an automatic frequency-sweeping SQUID susceptometer. Below Tλ = 2.17 K the relaxation rate τ -1 displays an exponential temperature dependence given by τ-1 = ω0 exp(- E/ kT) where ω0 = 2.48 × 10 4 s -1 and E/ k = 3.62 K, the activation energy of the relaxation process. Above Tλ broadened absorption curves and flattened Argand diagrams are observed. The ratio K1/ K2 (=0.22 ± 0.02) of the orthorhombic anisotropy constants and a weak power-law temperature dependence of the critical spin-flop field Hcr were determined.
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.
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 <
Oh, Joosung; Le, Manh Duc; Jeong, Jaehong; Lee, Jung-hyun; Woo, Hyungje; Song, Wan-Young; Perring, T G; Buyers, W J L; Cheong, S-W; Park, Je-Geun
2013-12-20
The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic LuMnO3, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin S=2. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120° spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal LuMnO3. Our results show that quasiparticles in a system hitherto thought of as "classical" can indeed break down. PMID:24483753
NASA Astrophysics Data System (ADS)
Li, P. H. Y.; Bishop, R. F.; Campbell, C. E.
2015-01-01
We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-1/2 J1-J2 Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J1>0 and J2≡κ J1>0 , respectively, in the window 0 ≤κ <1 . The classical version of the model has a single GS phase transition at κcl=1/8 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120∘ Néel order for κ <κcl to an infinitely degenerate family of 4-sublattice AFM Néel phases for κ >κcl . This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case κ =0 of the spin-1/2 model for the GS energy per spin, E /N =-0.5521 (2 ) J1 , and the GS magnetic order parameter, M =0.198 (5 ) (in units where the classical value is Mcl=1/2), which are among the best available. For the spin-1/2 J1-J2 model we find that the classical transition at κ =κcl is split into two quantum phase transitions at κ1c=0.060 (10 ) and κ2c=0.165 (5 ) . The two quasiclassical AFM states (viz., the 120∘ Néel state and the striped state) are found to be the stable GS phases in the regime κ <κ1c and κ >κ2c , respectively, while in the intermediate regimes κ1c<κ <κ2c the stable GS phase has no evident long-range magnetic order.
NASA Astrophysics Data System (ADS)
Bêche, B.; Gaviot, E.
2016-04-01
Within the Heisenberg's uncertainty principle it is explicitly discussed the impact of these inequalities on the theory of integrated photonics at sub-wavelength regime. More especially, the uncertainty of the effective index values in nanophotonics at sub-wavelength regime, which is defined as the eigenvalue of the overall opto-geometric problems in integrated photonics, appears directly stemming from Heisenberg's uncertainty. An apt formula is obtained allowing us to assume that the incertitude and the notion of eigenvalue called effective optical index or propagation constant is inversely proportional to the spatial dimensions of a given nanostructure yielding a transfer of the fuzziness on relevant senses of eigenvalues below a specific limit's volume.
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
Insight into photofragment vector correlation by a multi-center impulsive model.
Tsai, Po-Yu; Lin, King-Chuen
2015-07-15
A multi-center impulsive model has been recently developed to characterize the dynamic feature of product energy distribution in photodissociation of formaldehyde, H2CO → CO + H2. (J. Phys. Chem. A, 2015, 119, 29) The model is extended to predict the vector correlations among transition dipole moment μ of the parent molecule, recoil velocity v and rotational angular momentum j of the fragments produced via the transition state (TS) and roaming path. The correlation results of μ-j, j-j and μ-v vectors of the fragments are consistent with those reported using quasi-classical trajectory simulation on the global potential energy surface. In contrast to the TS route, the vector properties via the roaming path are loosely correlated. This work offers an alternative method to study stereodynamics of the photodissociation process, and is conducive to clarifying the origin of photofragment vector correlation especially for the roaming pathway. PMID:26150201
Heat Conductivity of the Heisenberg Spin-1/2 Ladder: From Weak to Strong Breaking of Integrability.
Steinigeweg, Robin; Herbrych, Jacek; Zotos, Xenophon; Brenig, Wolfram
2016-01-01
We investigate the heat conductivity κ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of interchain coupling J(⊥), by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction κ∝J(⊥)(-2), based on simple golden-rule arguments and valid in the strict limit J(⊥)→0, applies to a remarkably wide range of J(⊥), qualitatively and quantitatively. In the large J(⊥) limit, we show power-law scaling of opposite nature, namely, κ∝J(⊥)(2). Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at J(⊥)=J(∥). Reducing temperature T, starting from T=∞, this minimum scales as κ∝T(-2) down to T on the order of the exchange coupling constant. These results provide for a comprehensive picture of κ(J(⊥),T) of spin ladders. PMID:26799041
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)
Gu, Bo; Su, Gang; Gao, Song
2006-04-01
The magnetization process, the susceptibility, and the specific heat of the spin- 1/2 antiferromagnet (AF)-AF-ferromagnet (F) and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at m=1/6 for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.
Magnetic excitation spectrum of the square lattice S=1/2 Heisenberg antiferromagnet K2V3O8
NASA Astrophysics Data System (ADS)
Lumsden, M. D.; Nagler, S. E.; Sales, B. C.; Tennant, D. A.; McMorrow, D. F.; Lee, S.-H.; Park, S.
2006-12-01
We have explored the magnetic excitation spectrum of the S=1/2 square lattice Heisenberg antiferromagnet, K2V3O8 , using both triple-axis and time-of-flight inelastic neutron scattering. The long-wavelength spin waves are consistent with the previously determined Hamiltonian for this material. A small energy gap of 72±9μeV is observed at the antiferromagnetic zone center and the near-neighbor exchange constant is determined to be 1.08±0.03meV . A finite ferromagnetic interplanar coupling is observed along the crystallographic c axis with a magnitude of Jc=-0.0036±0.0006meV . However, upon approaching the zone boundary, the observed excitation spectrum deviates significantly from the expectation of linear spin wave theory resulting in split modes at the (π/2,π/2) zone boundary point. The effects of magnon-phonon interaction, orbital degrees of freedom, multimagnon scattering, and dilution/site randomness are considered in the context of the mode splitting. Unfortunately, no fully satisfactory explanation of this phenomenon is found and further theoretical and experimental work is needed.
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.
Recollections of Physics and of Physicists During the 1920's
ERIC Educational Resources Information Center
Dennison, David M.
1974-01-01
Presents the author's recollections of the emergence of the new quantum theory and his associations with such men as Oskar Klein, Niels Bohr, Frederick Hund, Werner Heisenberg, J. J. Thomson, and others. (GS)
NASA Astrophysics Data System (ADS)
Laflorencie, Nicolas; Luitz, David J.; Alet, Fabien
2015-09-01
Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the Néel ordered J1-J2 Heisenberg antiferromagnet on the square lattice. Different kinds of subsystem geometries are studied, either corner-free (line, strip) or with sharp corners (square). Contributions from the nG=2 Nambu-Goldstone modes give additive logarithmic corrections with a prefactor nG/2 independent of the Rényi index. On the other hand, π /2 corners lead to additional (negative) logarithmic corrections with a prefactor lqc which does depend on both nG and the Rényi index q , in good agreement with scalar field theory predictions. By varying the second neighbor coupling J2 we also explore universality across the Néel ordered side of the phase diagram of the J1-J2 antiferromagnet, from the frustrated side 0
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)
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.
Form factors in SU(3)-invariant integrable models
NASA Astrophysics Data System (ADS)
Belliard, S.; Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.
2013-04-01
We study SU(3)-invariant integrable models solvable by a nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.
NASA Astrophysics Data System (ADS)
Pires, Antonio; Sousa, Griffith
2014-03-01
The square lattice antiferromagnet with next and next nearest neighbor exchange interaction has been the subject of intense research in the last years. It can present the behavior of a frustrated system and can otherwise describe real materials. However, a large part of the work has been dedicated to spin 1/2 and done at zero temperature. A system with spin 1 is of interest because it can have a single ion anisotropy. To study these models simple approaches which yield an analytical description are very useful for practical purposes. Here we use a Modified Spin Wave theory, where corrections owing to spin wave interactions are taken into account self-consistently, to study the easy axis two dimensional spin 1 antiferromagnet with competing interaction and single ion anisotropy. We calculate the phase diagram at zero temperature, and several thermodynamic quantities such as the magnetization, the gap and the specific heat. Their relations with the temperature and anisotropy parameter are analyzed over the entire range of temperature. We have found a Neel and a collinear phase separated by a disordered phase. This disordered phase could be a candidate for a spin liquid. This work was partially supported by CNPQ, FAPEMIG and FAPEAM.
Thermodynamic properties of a layered S = 7/2 Heisenberg magnet Gd(OH)CO3
NASA Astrophysics Data System (ADS)
Orendac, Martin; Ulicny, Martin; Cizmar, Erik; Orendacova, Alzbeta; Chen, Yan-Cong; Meng, Zhao-Sha; Tong, Ming-Liang
2015-03-01
Thermodynamic quantities and ESR spectra of Gd(OH)CO3 (I) are reported. The material may be considered to consist of weakly coupled layers with potentially triangular arrangement of exchange paths within each layer. Different bridging groups and distances among Gd3+ ions may be responsible for spatial anisotropy of magnetic coupling. Preliminary analysis of magnetic susceptibility using Curie-Weiss law yielded θ = -1.05 K indicating weak antiferromagnetic coupling and consequently, spin frustration in (I). More detailed simultaneous analysis of specific heat, susceptibility and magnetization studied down to nominally 0.45 K revealed non-negligible role of single-ion anisotropy. Using the model of weakly interacting S =7/2 trimers, the gross features of measured data may be explained while assuming single-ion anisotropy D /kB ~ 0.6 K and effective intratrimer magnetic coupling | J /kB | ~0.3 K. The obtained D value reasonably reproduces the position and shape of ESR line. The performed analysis suggests that magnetism in (I) is governed predominantly by crystal field effects and frustration plays a minor role. Supported by ITMS26220120005 and VEGA 1/0143/13.
Semi-Classical Models for Virtual Antiparticle Pairs
NASA Technical Reports Server (NTRS)
Batchelor, David; Zukor, Dorothy (Technical Monitor)
2001-01-01
Virtual particle-antiparticle pairs of massive elementary particle& are predicted in Quantum Field Theory (QFT) to appear from the vacuum and annihilate each other again within their Heisenberg lifetimes h/4mc(exp 2). In this work, semiclassical models of this process - for the cases of massive leptons, quarks, and the massive weak bosons W and Z - are constructed. It is shown that the dynamical lifetime of the particle- antiparticle system in each case equals the Heisenberg lifetime to good approximation, and obeys appropriate quantization conditions on the field fluctuation action. In other words, the dynamical lifetime of the semiclassical model agrees with QED and QCD to good approximation. But the formula for the dynamical lifetime in each model includes the force strength coupling constant (e in the lepton case, alpha(sup s) (q(exp 2)) in the quark cases), while the Heisenberg lifetime formula does not. Observing the agreement of the Heisenberg and dynamical lifetimes, we may derive the QED and QCD coupling constants in terms of h, c, and numerical factors only.
Mechanisms of finite-temperature magnetism in the three-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Hirschmeier, Daniel; Hafermann, Hartmut; Gull, Emanuel; Lichtenstein, Alexander I.; Antipov, Andrey E.
We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be consistent with Heisenberg physics down to an interaction of U/t=10.
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)
Quigg, Chris
2011-04-01
The Large Hadron Collider at CERN is moving the experimental frontier of particle physics to the domain of electroweak symmetry breaking, reaching energies around one trillion electron volts for collisions among the basic constituents of matter. We do not know what the new wave of exploration will find, but the discoveries we make and the new puzzles we encounter are certain to change the face of particle physics and echo through neighboring sciences. In this new world, we confidently expect to learn what sets electromagnetism apart from the weak interactions, with profound implications for deceptively simple questions: Why are there atoms? Why chemistry? What makes stable structures possible? A pivotal step will be finding the Higgs boson-or whatever takes its place -and exploring its properties. But we hope for much more. More predictive extensions of the electroweak theory, including dynamical symmetry breaking and supersymmetry, imply new kinds of matter that would be within reach of LHC experiments. We suspect that candidates for the dark matter of the Universe could also await discovery on the TeV scale. The strong interactions may hold their own surprises. As we unravel the riddle of electroweak symmetry breaking, prospects arise for other new insights: into the different forms of matter, the unity of quarks and leptons, and the nature of spacetime. The questions in play all seem linked to one another-and to the kinship of the weak and electromagnetic interactions. I will speak of the evolving dialogue between theory and experiment, highlighting the work before us. Fermilab is operated by the Fermi Research Alliance under contract no. DE-AC02-07CH11359 with the U.S. Department of Energy.
J. J. Sakurai Prize for Theoretical Particle Physics Talk: Physics with Hadron colliders
NASA Astrophysics Data System (ADS)
Hinchliffe, Ian
2011-04-01
After many years of sustained effort, The LHC has started operation and physics results have started to be released. This marks the beginning of a new era in High Energy Physics during which the fundamental mechanism underlying the source of masses for the elextro-weak gauge bosons will be probed exhaustively. These results will, over the next decade, enable questions such as ``Does the Higgs boson exist?'' ``Are there extra space time dimensions,'' ``Is there supersymmetry?'' ``can dark matter be produced at a particle accelerator?'' to be addressed, and the large variety of theoretical ideas developed over the last 20 years to be ``weighed in the balance.'' My presentation will discuss some of the physics program of the ATLAS experiment, the discoveries that we expect to make in the next few years and their role in the ``weighing'' that will occur.
The education of an astronomical maverick: T. J. J. See and the University of Missouri
NASA Astrophysics Data System (ADS)
Peterson, Charles J.
2004-08-01
The educational background of the controversial astronomer Thomas Jefferson Jackson See is recounted. See failed in successive employment and research opportunities; coworkers and superiors apparently were repelled by his intense egotism, his inability to work with others, his refusal to operate within established codes of conduct, and questions arising from both the source and the reliability of his scientific work. See's approach to his scientific career was shaped, to a large degree, by his undergraduate education, and the professional turmoil of his later life was paralleled by his tumultuous career as a student at the University of Missouri, which included bitter political infighting and accusations of plagiarism. Combined with a tendency to make fundamental errors in both observational and theoretical research, See's flaws ultimately cost him his scientific credibility and destroyed his professional career and reputation.
J. J. Sakurai Prize: Scattering Amplitudes - the Story of Loops and Legs
NASA Astrophysics Data System (ADS)
Dixon, Lance
2014-03-01
Scattering amplitudes are at the interface between quantum field theory and particle experiment. Precise predictions for reactions at energy frontier machines such as the Large Hadron Collider (LHC) rely on quantum corrections to scattering amplitudes involving multiple quarks and gluons, as well as other particles. For decades, theorists used Feynman diagrams for this job. However, Feynman diagrams are just too slow, even on fast computers, to allow adequate precision for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past two decades, alternative methods to Feynman diagrams have come to fruition. The new ``on-shell'' methods are based on the old principle of unitarity. They can be much more efficient because they exploit the underlying simplicity of scattering amplitudes, and recycle lower-loop information. The same methods have also enabled new insight into the structure of gauge theory and gravity at the quantum level, especially in highly supersymmetric theories where they maintain all of the symmetries. I'll give a brief motivation for and introduction to the new methods, which will be followed by descriptions of their phenomenological and formal applications by David Kosower and Zvi Bern.
Form factors in quantum integrable models with GL(3)-invariant R-matrix
NASA Astrophysics Data System (ADS)
Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.
2014-04-01
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.
The origins of quantum interference and uncertainty broadening. A linear ribbon model approach
Tang, J.
1996-02-01
As an alternative to the orthodox Schroedinger wave mechanics or Heisenberg matrix mechanics approach, a simple linear ribbon model for quantum theory is presented. A different perspective and better physical insights into the origins of quantum interference and the mechanisms for uncertainty broadening are offered. Quantum interference in the atomic scale and superconducting behaviour in the macroscopic scale are compared.
The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
NASA Astrophysics Data System (ADS)
Belliard, S.; Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.
2012-10-01
We study SU(3)-invariant integrable models solvable by a nested algebraic Bethe ansatz. We obtain a determinant representation for the particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.
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.
NASA Astrophysics Data System (ADS)
Liu, Jin Hua; Wang, Hai Tao
2015-10-01
Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c = 1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class.
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.
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.
Peric, Mirna; Bales, Barney L; Peric, Miroslav
2012-01-01
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 (DD) interactions on 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 HSE and DD have been derived. By employing non-linear 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 if this discrepancy is due to inadequate analysis of the experimental data or an incomplete theory. A key new 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 illustrate the separation in this
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
NASA Astrophysics Data System (ADS)
Payen, C.; Mutka, H.; Soubeyroux, J. L.; Molinié, P.; Colombet, P.
1992-02-01
Differences in behaviour between the two quasi-1D Heisenberg antiferromagnets AgVP 2S 6 ( S=1) and AgCrP 2S 6 ( S = 3/2) have been evidenced by susceptibility measurements, neutron powder diffraction and inelastic neutron scattering. The results obtained for the S=1 compound are consistent with Haldane's conjecture as well as existing numerical results. The S = 3/2 compound behaves conventionally above the 3D ordering temperature ( TN=20 K).
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. PMID:25675728
NASA Astrophysics Data System (ADS)
Hammar, P. R.; Dender, D. C.; Broholm, C.; Reich, D. H.
1997-03-01
Copper Benzoate is an established S=1/2 linear antiferromagnetic Heisenberg spin chain. A recent inelastic neutron scattering experiment found low lying excitations at incommensurate wave vectors in a magnetic field.(D. C. Dender, P. R. Hammar, C. Broholm, D. H. Reich, G. Aeppli, (to be published)) However, contrary to theoretical predictions,(G. Müller, H. Thomas, H. Beck, J. C. Bonner, Phys. Rev. B 24) 1428 (1981). this experiment showed a field-induced gap in the magnetic excitation spectrum. We present heat capacity data that explore the evolution of this gap with applied magnetic field. The gap is highly dependent on field direction, and is a result of the relative anisotropies in the plane perpendicular to the field. The gaps in the largest field measured (H = 8.8 T) are Δb = 2.81 K, Δ_a^'' = 1.57(5) K, and Δ_c^'' = 5.4(1) K where b, c^'' and a^'' are the antiferromagnetic principal axes.
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
Finite temperature spin-dynamics and phase transitions in spin-orbital models
Chen, C.-C.
2010-04-29
We study finite temperature properties of a generic spin-orbital model relevant to transition metal compounds, having coupled quantum Heisenberg-spin and Ising-orbital degrees of freedom. The model system undergoes a phase transition, consistent with that of a 2D Ising model, to an orbitally ordered state at a temperature set by short-range magnetic order. At low temperatures the orbital degrees of freedom freeze-out and the model maps onto a quantum Heisenberg model. The onset of orbital excitations causes a rapid scrambling of the spin spectral weight away from coherent spin-waves, which leads to a sharp increase in uniform magnetic susceptibility just below the phase transition, reminiscent of the observed behavior in the Fe-pnictide materials.
Analysis of quantum spin models on hyperbolic lattices and Bethe lattice
NASA Astrophysics Data System (ADS)
Daniška, Michal; Gendiar, Andrej
2016-04-01
The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the tensor product variational formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces mean-field-like behavior of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence.
Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model
NASA Astrophysics Data System (ADS)
Fatah, Aziz H.; Radhi, R. A.; Abdullah, Nzar R.
2016-07-01
We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)dr m where f(r) = rμ, rμ jJ(qr), V(r) corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition, we take into account a general integral formula of the matrix element
Coarse-grained modeling of DNA curvature
NASA Astrophysics Data System (ADS)
Freeman, Gordon S.; Hinckley, Daniel M.; Lequieu, Joshua P.; Whitmer, Jonathan K.; de Pablo, Juan J.
2014-10-01
The interaction of DNA with proteins occurs over a wide range of length scales, and depends critically on its local structure. In particular, recent experimental work suggests that the intrinsic curvature of DNA plays a significant role on its protein-binding properties. In this work, we present a coarse grained model of DNA that is capable of describing base-pairing, hybridization, major and minor groove widths, and local curvature. The model represents an extension of the recently proposed 3SPN.2 description of DNA [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)], into which sequence-dependent shape and mechanical properties are incorporated. The proposed model is validated against experimental data including melting temperatures, local flexibilities, dsDNA persistence lengths, and minor groove width profiles.
Quantum statistical foundation to the Fermi liquid model and Ginzburg-Landau wave function
Fujita, Shigeji; Godoy, S. )
1993-12-01
An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in the k-space is given, starting with a realistic model of a metal including the Coulomb interaction among and between electrons and lattice-ions. The Ginzburg-Landau wave function [Psi][sub [sigma
Fermionization and Hubbard models
NASA Astrophysics Data System (ADS)
Dargis, P.; Maassarani, Z.
1998-12-01
We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this method on various integrable and non-integrable chains, and deduce some general results. In particular, we fermionize XXC spin-chains and study their symmetries. Fermionic realizations of certain Lie algebras and superalgebras appear naturally as symmetries of some models. We also fermionize recently obtained Hubbard models, and obtain for the first time multispecies analogues of the Hubbard model, in their fermionic form. We comment on the conflict between symmetry enhancement and integrability of these models. Finally, the fermionic versions of the non-integrable spin-1 and spin- {3}/{2} Heisenberg chains are obtained.
NASA Astrophysics Data System (ADS)
Ni, Hui-Ying; Fang, Jian-Xing; Zhu, Shi-Qun; Sha, Jin-Qiao; Jiang, Wei-Xing
2008-02-01
In this paper we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component JZ, the inhomogeneous magnetic field b, the anisotropy γ, and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fa. High average fidelity of the teleportation is obtained when the temperat ure is very low. Under some condition, we also find that when inhomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.
NASA Astrophysics Data System (ADS)
Brandt, Jørgen; Andersen, Mikael S.; Bønløkke, Jakob; Christensen, Jesper H.; Hansen, Kaj M.; Hertel, Ole; Im, Ulas; Jensen, Steen S.; Ketzel, Matthias; Nielsen, Ole-Kenneth; Plejdrup, Marlene S.; Sigsgaard, Torben; Geels, Camilla
2015-04-01
We have developed an integrated health impact assessment system EVA (Economic Valuation of Air pollution; Brandt et al., 2013a; 2013b), based on the impact-pathway chain, to assess the health impacts and health-related economic externalities of air pollution resulting from specific emission sources or sectors. The system is used to support policymaking with respect to emission control. The EVA system has previously been used to assess the health impacts based on results from a regional model DEHM (the Danish Eulerian Hemispheric Model; Brandt et al., 2012). In this study we have used a coupling of two chemistry transport models to calculate the air pollution concentration at different scales; the DEHM model to calculate the air pollution levels with a resolution down to 5.6 km x 5.6 km and the UBM model (Urban Background Model ; Berkowicz, 2000; Brandt et al., 2001) to further calculate the air pollution at 1 km x 1 km resolution for Denmark using results from DEHM as boundary conditions. Both the emission data based on the SPREAD model (Plejdrup and Gyldenkærne, 2011) as well as the population density has been represented in the model system with the same high resolution. The new developments of the integrated model system will be presented as well as results for health impacts and related external costs over the years 2006-2014 for Denmark. Furthermore, a sensitivity study of the health impact using coarse and fine resolutions in the model system has been carried out to evaluate the effect of improved description of the geographical population distribution with respect to location of local emissions. References Berkowicz, R., 2000. A Simple Model for Urban Background Pollution. Environmental Monitoring and Assessment, 65, 1/2, 259-267. Brandt, J., J. H. Christensen, L. M. Frohn, F. Palmgren, R. Berkowicz and Z. Zlatev, 2001: "Operational air pollution forecasts from European to local scale". Atmospheric Environment, Vol. 35, Sup. No. 1, pp. S91-S98, 2001 Brandt
Generic spin model for the honeycomb iridates beyond the Kitaev limit
NASA Astrophysics Data System (ADS)
Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young
2014-03-01
Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the jeff = 1 / 2 Mott insulator in these materials exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here we provide the generic nearest-neighbour spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit we find new magnetic phases: 120° and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.
Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit
NASA Astrophysics Data System (ADS)
Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young
2014-02-01
Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the jeff=1/2 Mott insulator in these materials, exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here, we provide the generic nearest-neighbor spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond-dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120° and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.
Multiscale Modeling of Molecular Magnets
Ramasesha, S.; Raghunathan, Rajamani
2007-11-29
Here, we present an overview of methods of modeling Molecular Magnets in different length scales. First, we discuss a microscopic model to understand the nature of superexchange interaction in binuclear transition metal complexes of different geometry viz. A-B, A-B-A, B-A-B, linear A-B-A-B, and cyclic A-B-A-B systems. We obtain the quantum phase diagrams along various planes in the parameter space and identify the various model parameters which control the nature of superexchange in these systems. We also obtain contours of effective superexchange constants. In the next section we discuss the method of full symmetry adaptation in Valence Bond method to obtain the low-lying eigenstates of the Heisenberg spin Hamiltonian of large systems. The third part of this article deals with the calculation of the magnetic anisotropy parameters (D{sub M} and E{sub M}) of Single Molecule Magnets (SMMs). We use the single ion anisotropy values to obtain D{sub M} and E{sub M} values of the SMM, using a perturbative approach. We first solve the unperturbed Hamiltonian which is a simple spin Heisenberg Hamiltonian. Then we introduce the perturbing term H{sub 1} consisting of the single ion anisotropy. We then solve for the molecular anisotropy parameters by equating two different ways for computing the matrix elements of the perturbation term, from knowledge of the spin-spin correlation functions and the direction of orientation of the single ion anisotropies.
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
The Landau-Lifshitz equation in atomistic models
NASA Astrophysics Data System (ADS)
Ellis, M. O. A.; Evans, R. F. L.; Ostler, T. A.; Barker, J.; Atxitia, U.; Chubykalo-Fesenko, O.; Chantrell, R. W.
2015-09-01
The Landau-Lifshitz (LL) equation, originally proposed at the macrospin level, is increasingly used in Atomistic Spin Dynamic (ASD) models. These models are based on a spin Hamiltonian featuring atomic spins of fixed length, with the exchange introduced using the Heisenberg formalism. ASD models are proving a powerful approach to the fundamental understanding of ultrafast magnetization dynamics, including the prediction of the thermally induced magnetization switching phenomenon in which the magnetization is reversed using an ultra-fast laser pulse in the absence of an externally applied field. This paper outlines the ASD model approach and considers the role and limitations of the LL equation in this context.
Correlation functions of integrable models: A description of the ABACUS algorithm
NASA Astrophysics Data System (ADS)
Caux, Jean-Sébastien
2009-09-01
Recent developments in the theory of integrable models have provided the means of calculating dynamical correlation functions of some important observables in systems such as Heisenberg spin chains and one-dimensional atomic gases. This article explicitly describes how such calculations are generally implemented in the ABACUS C++ library, emphasizing the universality in treatment of different cases coming as a consequence of unifying features within the Bethe ansatz.
A review of mesospheric and lower thermosphere models
NASA Astrophysics Data System (ADS)
Portnyagin, Yuri
2006-01-01
The empirical mesosphere/lower thermosphere (MLT) models, in particular Fleming et al. [Fleming, E.L., Chandra, S., Schoeberl, M.R., Barnett, J.J. Monthly mean global climatology of temperature, wind, geopotential height and pressure for 0-120 km. NASA Technical Memorandum 100697, 1988; Fleming, E.L., Chandra, S., Barnett, J.J., Corney, M. Zonal mean temperature, pressure, zonal wind and geopotential height as function of latitude. Adv. Space Res., 10 (12), 11-59, 1990.], HWM-93 [Hedin, A.E., Fleming, E.L., Manson, A.H., Schmidlin, F.J., Avery, S.K., Clark, R.R., Franke, S.J., Fraser, G.J., Tsuda, T., Vial, F., Vincent, R.A. Empirical wind model for the middle and lower atmosphere. J. Atmos.Terr. Phys., 58, 1421-1447, 1996] and GEWM [Portnyagin, Yu.I, Solovjova, T., Merzlyakov, E., et al., Mesosphere/lower thermosphere prevailing wind model. Adv. Space Res., 34, 1755-1762, 2004] models, are compared. The main reasons of the differences between the models are discussed. These reasons are mainly connected with the differences between the used ground- and space-based datasets, including the systematic biases between the ground-based and space-based measurements, and with the different methods of the data assimilation. The effects of year-to-year wind variations and the longitudinal prevailing wind variability, as well as the effects of non-migrating tides in construction of the climatic empirical models is not so strong. The recommendation to construct a new and updated CIRA wind model for the MLT region has been followed.
NASA Astrophysics Data System (ADS)
Ortiz, E.; Guna, V.
2009-04-01
The present work aims to carry out a comparison between two distributed hydrological models, the TOPKAPI (Ciarapica and Todini, 1998; Todini and Ciarapica, 2001) and TETIS (Vélez, J. J.; Vélez J. I. and Francés, F, 2002) models, obtaining the hydrological solution computed on the basis of the same storm events. The first model is physically based and the second one is conceptually based. The analysis was performed on the 21,4 km2 Goodwin Creek watershed, located in Panola County, Mississippi. This watershed extensively monitored by the Agricultural Research Service (ARS) National Sediment Laboratory (NSL) has been chosen because it offers a complete database compiling precipitation (16 rain gauges), runoff (6 discharge stations) and GIS data. Three storm events were chosen to evaluate the performance of the two models: the first one was chosen to calibrate the models, and the other two to validate them. Both models performed a satisfactory hydrological response both in calibration and validation events. While for the TOPKAPI model it wasn't a real calibration, due to its really good performance with parameters modal values derived of watershed characteristics, for the TETIS model it has been necessary to perform a previous automatic calibration. This calibration was carried out using the data provided by the observed hydrograph, in order to adjust the modeĺs 9 correction factors. Keywords: TETIS, TOPKAPI, distributed models, hydrological response, ungauged basins.
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.
Sargeant, G.A.
2002-01-01
Review of: Millspaugh, Joshua J., and John M. Marzluff, editors. 2001. Radio tracking and animal populations. Academic Press, San Diego, California. xvii 1 474 p. $69.95 (alk. paper), ISBN: 0-12-497781-2.
NASA Astrophysics Data System (ADS)
Ellis, R. Keith
2009-05-01
Recent progress in perturbative QCD is described, with special emphasis on one-loop corrections to processes with large numbers of jets. These processes constitute important backgrounds for new physics searches at hadron colliders.
Generic model for the hyperkagome iridate Na4Ir3O8 in the local-moment regime
NASA Astrophysics Data System (ADS)
Mizoguchi, Tomonari; Hwang, Kyusung; Lee, Eric Kin-Ho; Kim, Yong Baek
2016-08-01
The hyperkagome iridate, Na4Ir3O8 , has been regarded as a promising candidate material for a three-dimensional quantum spin liquid. Here the three-dimensional network of corner-sharing triangles forms the hyperkagome lattice of Ir4 + ions. Due to strong spin-orbit coupling, the local moments of Ir4 + ions are described by the pseudospin jeff=1 /2 Kramers doublet. The Heisenberg model on this lattice is highly frustrated, and quantum/classical versions have been studied in earlier literature. In this work, we derive a generic local-moment model beyond the Heisenberg limit for the hyperkagome iridate by considering multiorbital interactions for all the t2 g orbitals and spin-orbit coupling. The lifting of massive classical degeneracy in the Heisenberg model by various spin-anisotropy terms is investigated at the classical level, and the resulting phase diagram is presented. We find that different anisotropy terms prefer distinct classes of magnetically ordered phases, often with various discrete degeneracy. The implications of our results for recent μ SR and NMR experiments on this material and possible quantum spin liquid phases are discussed.
Derivation of effective spin models from a three band model for CuO
NASA Astrophysics Data System (ADS)
Müller-Hartmann, E.; Reischl, A.
2002-07-01
The derivation of effective spin models describing the low energy magnetic properties of undoped CuO2-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La2CuO4. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping tpd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Padé approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Padé approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor Heisenberg model is emphasized.
Itoh, S.; Nakayama, T.; Kajimoto, R.; Adams, M. A.; Materials Science Division; High Energy Accelerator Research Organization; Rutherford Appleton Lab.
2009-01-01
The dynamic structure factors S(q,w) of an ideal percolating network, the three-dimensional (3d) dilute Heisenberg antiferromagnet RbMn{sub 0.4}Mg{sub 0.6}F{sub 3}, obtained from high resolution ({Delta}E = 17.5 {micro}eV) inelastic neutron scattering (INS) experiments are analyzed for the first time within the framework of the single-length-scaling postulate (SLSP). The analysis confirms the validity of the SLSP and is also used to extract the values of the key exponents governing the spin dynamics, the dynamic exponent (z{sub AF} = D{sub f}/tilded{sub AF}) being 2.5 {+-} 0.1 and the spectral dimension tilded{sub AF} for antiferromagnetic (AFM) fractons taking a value of unity.
Integrable models and combinatorics
NASA Astrophysics Data System (ADS)
Bogolyubov, N. M.; Malyshev, C. L.
2015-10-01
Relations between quantum integrable models solvable by the quantum inverse scattering method and some aspects of enumerative combinatorics and partition theory are discussed. The main example is the Heisenberg XXZ spin chain in the limit cases of zero or infinite anisotropy. Form factors and some thermal correlation functions are calculated, and it is shown that the resulting form factors in a special q-parametrization are the generating functions for plane partitions and self-avoiding lattice paths. The asymptotic behaviour of the correlation functions is studied in the case of a large number of sites and a moderately large number of spin excitations. For sufficiently low temperature a relation is established between the correlation functions and the theory of matrix integrals. Bibliography: 125 titles.
Effective action for noncommutative Bianchi I model
NASA Astrophysics Data System (ADS)
Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.
2013-06-01
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.
Effective action for noncommutative Bianchi I model
Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.
2013-06-12
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.
Strong coupling theory for electron-mediated interactions in double-exchange models
NASA Astrophysics Data System (ADS)
Ishizuka, Hiroaki; Motome, Yukitoshi
2015-07-01
We present a theoretical framework for evaluating effective interactions between localized spins mediated by itinerant electrons in double-exchange models. Performing the expansion with respect to the spin-dependent part of the electron hopping terms, we show a systematic way of constructing the effective spin model in the large Hund's coupling limit. As a benchmark, we examine the accuracy of this method by comparing the results with the numerical solutions for the spin-ice type model on a pyrochlore lattice. We also discuss an extension of the method to the double-exchange models with Heisenberg and X Y localized spins.
An interactive modelling tool for understanding hydrological processes in lowland catchments
NASA Astrophysics Data System (ADS)
Brauer, Claudia; Torfs, Paul; Uijlenhoet, Remko
2016-04-01
Recently, we developed the Wageningen Lowland Runoff Simulator (WALRUS), a rainfall-runoff model for catchments with shallow groundwater (Brauer et al., 2014ab). WALRUS explicitly simulates processes which are important in lowland catchments, such as feedbacks between saturated and unsaturated zone and between groundwater and surface water. WALRUS has a simple model structure and few parameters with physical connotations. Some default functions (which can be changed easily for research purposes) are implemented to facilitate application by practitioners and students. The effect of water management on hydrological variables can be simulated explicitly. The model description and applications are published in open access journals (Brauer et al, 2014). The open source code (provided as R package) and manual can be downloaded freely (www.github.com/ClaudiaBrauer/WALRUS). We organised a short course for Dutch water managers and consultants to become acquainted with WALRUS. We are now adapting this course as a stand-alone tutorial suitable for a varied, international audience. In addition, simple models can aid teachers to explain hydrological principles effectively. We used WALRUS to generate examples for simple interactive tools, which we will present at the EGU General Assembly. C.C. Brauer, A.J. Teuling, P.J.J.F. Torfs, R. Uijlenhoet (2014a): The Wageningen Lowland Runoff Simulator (WALRUS): a lumped rainfall-runoff model for catchments with shallow groundwater, Geosci. Model Dev., 7, 2313-2332. C.C. Brauer, P.J.J.F. Torfs, A.J. Teuling, R. Uijlenhoet (2014b): The Wageningen Lowland Runoff Simulator (WALRUS): application to the Hupsel Brook catchment and Cabauw polder, Hydrol. Earth Syst. Sci., 18, 4007-4028.
String-charge duality in integrable lattice models
NASA Astrophysics Data System (ADS)
Ilievski, Enej; Quinn, Eoin; De Nardis, Jacopo; Brockmann, Michael
2016-06-01
We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ spin chain. As an application we discuss a quantum quench scenario, in both the gapped and critical regimes. We outline an exact technique which allows for an efficient implementation on periodic matrix product states. In addition, for certain simple product states we obtain analytic closed-form expressions in terms of solutions to Hirota functional relations. Remarkably, no reference to a maximal entropy principle is invoked.
A nonlinear Bloch model for Coulomb interaction in quantum dots
Bidegaray-Fesquet, Brigitte Keita, Kole
2014-02-15
In this paper, we first derive a Coulomb Hamiltonian for electron–electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix. The coupling with Maxwell equations in case of interaction with an electromagnetic field is also considered from the Cauchy problem point of view. The study is completed by numerical results and a discussion about the advisability of neglecting intra-band coherences, as is done in part of the literature.
Wang-Landau Algorithm for Continuous Models and Joint Density of States
Zhou, Chenggang; Schulthess, Thomas C; Torbrugge, S.; Landau, D. P.
2006-01-01
We present a modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states of ferromagnet Heisenberg models and a model polymer chain. The joint density of states contains more information than the density of states of a single variable-energy, but is also much more time consuming to calculate. We present strategies to significantly speed up this calculation for large systems over a large range of energy and order parameter.
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. PMID:7330097
NASA Astrophysics Data System (ADS)
Baranová, Lucia; Orendáčová, Alžbeta; Čižmár, Erik; Tarasenko, Róbert; Tkáč, Vladimír; Orendáč, Martin; Feher, Alexander
2016-04-01
Organo-metallic compounds Cu(en)(H2O)2SO4 (en=C2H8N2) and Cu(tn)Cl2 (tn=C3H10N2) representing S=1/2 quasi-two-dimensional Heisenberg antiferromagnets with an effective intra-layer exchange coupling J/kB≈3 K, have been examined by specific heat measurements at temperatures down to nominally 50 mK and magnetic fields up to 14 T. A comparative analysis of magnetic specific heat in zero magnetic field revealed nearly identical contribution of short-range magnetic correlations and significant differences were observed at lowest temperatures. A phase transition to long-range order was observed in Cu(en)(H2O)2SO4 at TC=0.9 K while hidden in Cu(tn)Cl2. A response of both compounds to the application of magnetic field has rather universal features characteristic for a field-induced Berezinskii-Kosterlitz-Thouless transition theoretically predicted for ideal two-dimensional magnets.
NASA Astrophysics Data System (ADS)
Yang, Jin-Wei; Gao, Yi-Tian; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin
2016-01-01
In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple-dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.
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
NASA Astrophysics Data System (ADS)
Wang, Qi-Min; Gao, Yi-Tian; Su, Chuan-Qi; Mao, Bing-Qing; Gao, Zhe; Yang, Jin-Wei
2015-12-01
In this paper, a higher-order (2 + 1) -dimensional nonlinear Schrödinger-type equation is investigated, which describes the nonlinear spin dynamics of the (2 + 1) -dimensional Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction. Lax pair and infinite-number conservation laws are constructed, which could prove the existence of the multi-soliton solutions. Via the auxiliary function, bilinear forms and dark-soliton solutions are derived. Properties and interaction patterns for the dark solitons are investigated: (i) Effects on the dark solitons arising from the bilinear interaction, biquadratic interaction and lattice parameter are discussed. (ii) Through the asymptotic analysis, elastic and inelastic interaction between the two solitons is discussed analytically and graphically, respectively. Due to the elastic interaction, amplitudes and velocities of the two dark solitons remain unchanged with the distortion of the interaction area, except for certain phase shifts. However, in virtue of the inelastic interaction, amplitudes of the dark solitons reduce to zero, without the distortion. (iii) Elastic interaction among the three dark solitons is investigated, which implies that the properties of the elastic interaction among the three are similar to that between the two, except for the more complicated distortion. Inelastic-elastic interaction is also investigated, which implies that the interaction between the inelastic region and the dark soliton is elastic. (iv) Linear stability analysis is proposed, which is used to analyze the properties of modulation instability and proves that the dark solitons are modulationally stable.
Modelling sub-daily evaporation from a small reservoir.
NASA Astrophysics Data System (ADS)
McGloin, Ryan; McGowan, Hamish; McJannet, David; Burn, Stewart
2013-04-01
. Prairie, J. J. Cole, C. M. Duarte, L. J. Tranvik, R. G. Striegl, W. H. McDowell, P. Kortelainen, N. F. Caraco, J. M. Melack and J. J. Middelburg (2006), The global abundance and size distribution of lakes, ponds, and impoundments, Limnology and Oceanography, 51, 2388-2397. Granger, R.J. and N. Hedstrom (2011), Modelling hourly rates of evaporation from small lakes, Hydrological and Earth System Sciences, 15, doi:10.5194/hess-15-267-2011. Imberger, J. and J.C. Patterson (1981), Dynamic Reservoir Simulation Model - DYRESM: 5, In: Transport Models for Inland and Coastal Waters. H.B. Fischer (Ed.). Academic Press, New York, 310-361.
Phase diagram of a truncated tetrahedral model.
Krcmar, Roman; Gendiar, Andrej; Nishino, Tomotoshi
2016-08-01
Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analog of the entanglement entropy, which is numerically calculated by the corner transfer matrix renormalization group method. The obtained phase diagram consists of four different phases, which are separated by five transition lines. In the parameter region, where the octahedral anisotropy is dominant, a weak first-order phase transition is observed. PMID:27627273
Reconciling the 2 TeV excesses at the LHC in a linear seesaw left-right model
NASA Astrophysics Data System (ADS)
Deppisch, Frank F.; Graf, Lukas; Kulkarni, Suchita; Patra, Sudhanwa; Rodejohann, Werner; Sahu, Narendra; Sarkar, Utpal
2016-01-01
We interpret the 2 TeV excesses at the LHC in a left-right symmetric model with Higgs doublets and spontaneous D -parity violation. The light neutrino masses are understood via a linear seesaw, suppressed by a high D -parity breaking scale, and the heavy neutrinos have a pseudo-Dirac character. In addition, with a suppressed right-handed gauge coupling gR/gL≈0.6 in an S O (10 ) embedding, we can thereby interpret the observed e e j j excess at CMS. We show that it can be reconciled with the diboson and dijet excesses within a simplified scenario based on our model. Moreover, we find that the mixing between the light and heavy neutrinos can be potentially large, which would induce dominant nonstandard contributions to neutrinoless double beta decay via long-range λ and η neutrino exchange.
A Numerical Model for Atomtronic Circuit Analysis
Chow, Weng W.; Straatsma, Cameron J. E.; Anderson, Dana Z.
2015-07-16
A model for studying atomtronic devices and circuits based on finite-temperature Bose-condensed gases is presented. The approach involves numerically solving equations of motion for atomic populations and coherences, derived using the Bose-Hubbard Hamiltonian and the Heisenberg picture. The resulting cluster expansion is truncated at a level giving balance between physics rigor and numerical demand mitigation. This approach allows parametric studies involving time scales that cover both the rapid population dynamics relevant to nonequilibrium state evolution, as well as the much longer time durations typical for reaching steady-state device operation. This model is demonstrated by studying the evolution of a Bose-condensed gas in the presence of atom injection and extraction in a double-well potential. In this configuration phase locking between condensates in each well of the potential is readily observed, and its influence on the evolution of the system is studied.
Numerical model for atomtronic circuit analysis
NASA Astrophysics Data System (ADS)
Chow, Weng W.; Straatsma, Cameron J. E.; Anderson, Dana Z.
2015-07-01
A model for studying atomtronic devices and circuits based on finite-temperature Bose-condensed gases is presented. The approach involves numerically solving equations of motion for atomic populations and coherences, derived using the Bose-Hubbard Hamiltonian and the Heisenberg picture. The resulting cluster expansion is truncated at a level giving balance between physics rigor and numerical demand mitigation. This approach allows parametric studies involving time scales that cover both the rapid population dynamics relevant to nonequilibrium state evolution, as well as the much longer time durations typical for reaching steady-state device operation. The model is demonstrated by studying the evolution of a Bose-condensed gas in the presence of atom injection and extraction in a double-well potential. In this configuration phase locking between condensates in each well of the potential is readily observed, and its influence on the evolution of the system is studied.
Influence of magnetospheric inputs definition on modeling of ionospheric storms
NASA Astrophysics Data System (ADS)
Tashchilin, A. V.; Romanova, E. B.; Kurkin, V. I.
Usually for numerical modeling of ionospheric storms corresponding empirical models specify parameters of neutral atmosphere and magnetosphere. Statistical kind of these models renders them impractical for simulation of the individual storm. Therefore one has to correct the empirical models using various additional speculations. The influence of magnetospheric inputs such as distributions of electric potential, number and energy fluxes of the precipitating electrons on the results of the ionospheric storm simulations has been investigated in this work. With this aim for the strong geomagnetic storm on September 25, 1998 hour global distributions of those magnetospheric inputs from 20 to 27 September were calculated by the magnetogram inversion technique (MIT). Then with the help of 3-D ionospheric model two variants of ionospheric response to this magnetic storm were simulated using MIT data and empirical models of the electric fields (Sojka et al., 1986) and electron precipitations (Hardy et al., 1985). The comparison of the received results showed that for high-latitude and subauroral stations the daily variations of electron density calculated with MIT data are more close to observations than those of empirical models. In addition using of the MIT data allows revealing some peculiarities in the daily variations of electron density during strong geomagnetic storm. References Sojka J.J., Rasmussen C.E., Schunk R.W. J.Geophys.Res., 1986, N10, p.11281. Hardy D.A., Gussenhoven M.S., Holeman E.A. J.Geophys.Res., 1985, N5, p.4229.
Quantum phase transitions in the Fermi-Bose Hubbard model
Carr, L.D.; Holland, M.J.
2005-09-15
We propose a multiband Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two-state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
NASA Astrophysics Data System (ADS)
Cirilo António, N.; Manojlović, N.; Salom, I.
2014-12-01
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.
Modelling the oil spill track from Prestige-Nassau accident
NASA Astrophysics Data System (ADS)
Montero, P.; Leitao, P.; Penabad, E.; Balseiro, C. F.; Carracedo, P.; Braunschweig, F.; Fernandes, R.; Gomez, B.; Perez-Munuzuri, V.; Neves, R.
2003-04-01
. Prego, J.J. Taboada, P. Leitão, M. Ruiz-Villarreal, R. Neves and V. Pérez-Villar. Oceanologica Acta 22(2), p.167-177, (1999). (2) A model for ocean circulation on the Iberian Coast. H.S. Coelho, R.J.J. Neves, M. White, P.C. Leitão and A.J. Santos. Journal of Marine Systems 32, 153-179 (2002). (3) Impact of Cloud Analysis on Numerical Weather Prediction in the Galician Region of Spain. M.J. Souto, C.F. Balseiro, V. Pérez-Muñuzuri, M. Xue and K. Brewster, Journal of Applied Meteorology (2003)
Quantum Paramagnet in a π Flux Triangular Lattice Hubbard Model.
Rachel, Stephan; Laubach, Manuel; Reuther, Johannes; Thomale, Ronny
2015-04-24
We propose the π flux triangular lattice Hubbard model (π THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the π THM that we identify for intermediate Hubbard U is framed by a Dirac semimetal for weak coupling and by 120° Néel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the π THM maps to a Hubbard model which corresponds to the (J_{H},J_{K})=(-1,2) Heisenberg-Kitaev model in its strong coupling limit. The π THM provides a promising microscopic testing ground for exotic finite-U spin liquid ground states amenable to numerical investigation. PMID:25955072
Sr2Cu(PO4)2 and Ba2Cu(PO4)2 as quasi-one-dimensional spin-1/2 Heisenberg antiferromagnet
NASA Astrophysics Data System (ADS)
Haque, Md. Mahfoozul; Ahsan, M. A. H.
2016-03-01
Using magnetic exchange couplings for antiferromagnets Sr2Cu(PO4)2 and Ba2Cu(PO4)2, estimated independently by Johannes (2006 [1]) and Salunke (2007 [2]), we present model calculations via exact diagonalization for several lattices of 24 and 16 spins by calculating experimentally accessible quantities like spin-spin correlation, the antiferromagnetic order-parameter, entropy-density, specific-heat and z-component of the magnetic susceptibility using up to 15 low-lying eigenstates. From our calculation, the ratio of critical entropy and mean-field critical entropy comes out to be ∼ 0.492(7). The slope of the specific heat curve at low temperatures is found to be 2 / 3. The peak value of z-component of the magnetic susceptibility versus temperature curve turns out to be 1/3 χ ∼ 0.05 . Our results favor the conclusion that these magnetic compounds are indeed quasi-one-dimensional antiferromagnets.
Extending a rainfall-runoff model for lowland catchments from lumped to semi-distributed
NASA Astrophysics Data System (ADS)
Brauer, Claudia; Torfs, Paul; Teuling, Ryan; Uijlenhoet, Remko
2016-04-01
, A.J. Teuling, P.J.J.F. Torfs, R. Uijlenhoet (2014a): The Wageningen Lowland Runoff Simulator (WALRUS): a lumped rainfall-runoff model for catchments with shallow groundwater, Geosci. Model Dev., 7, 2313-2332. C.C. Brauer, P.J.J.F. Torfs, A.J. Teuling, R. Uijlenhoet (2014b): The Wageningen Lowland Runoff Simulator (WALRUS): application to the Hupsel Brook catchment and Cabauw polder, Hydrol. Earth Syst. Sci., 18, 4007-4028.
A time-invariant visco-elastic windkessel model relating blood flow and blood volume.
Zheng, Ying; Mayhew, John
2009-10-01
The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure-volume relationship of blood vessels is treated as a state variable dependent on the rate of change of CBV, producing hysteresis in the pressure-volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and
MHD results from a collisionless fluid model
NASA Astrophysics Data System (ADS)
Ramos, J. J.
2002-11-01
A non-conventional closure ansatz for collisionless MHD has been proposed in Ref.[1]. The truncation of the set of fluid moment equations is suggested by a comparison between the standard non-relativistic set and the non-relativistic limit of the relativistic set derived in Ref.[2]. The resulting model is a closed system of evolution equations in conservation form for the particle, momentum and energy densities, and the energy flux, allowing for pressure anisotropy and parallel heat flux. The static equilibrium condition is the same as in the Chew-Goldberger-Low theory, supplemented by the condition that the parallel energy flux be constant along the magnetic field. We study the linear perturbations about such static equilibria to derive the MHD wave dispersion relations in a homogeneous background and the perturbed potential energy associated with a stability energy principle. [1] J.J. Ramos, 2002 International Sherwood Theory Meeting, Rochester, NY, paper 1D25. [2] R.D. Hazeltine and S.M. Mahajan, Ap. J. 567, 1262 (2002).
First-principles study of the minimal model of magnetic interactions in Fe-based superconductors
NASA Astrophysics Data System (ADS)
Glasbrenner, J. K.; Velev, J. P.; Mazin, I. I.
2014-02-01
Using noncollinear first-principles calculations, we perform a systematic study of the magnetic order in several families of ferropnictides. We find a fairly universal energy dependence on the magnetization order in all cases. Our results confirm that a simple Heisenberg model fails to account for the energy dependence of the magnetization in a couple of ways: first, a biquadratic term is present in all cases and, second, the magnetic moment softens depending on the orientation. We also find that hole doping substantially reduces the biquadratic contribution, although the antiferromagnetic stripe state remains stable within the whole range of doping concentrations, and thus the reported lack of the orthorhombicity in Na-doped BaFe2As2 is probably due to factors other than a sign reversal of the biquadratic term. Finally, we discover that even with the biquadratic term, there is a limit to the accuracy of mapping the density functional theory energetics onto Heisenberg-type models, independent of the range of the model.
Chaos in a 4D dissipative nonlinear fermionic model
NASA Astrophysics Data System (ADS)
Aydogmus, Fatma
2015-12-01
Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.
Molecular modeling of fluoropropene refrigerants.
Raabe, Gabriele
2012-05-17
Different fluoropropenes are currently considered as refrigerants, either as pure compounds or as components in low GWP (global warming potential) refrigerant mixtures. Due to their limited commercial production, experimental data for the thermophysical properties of fluoropropenes and their mixtures are in general rare, which hampers the exploration of their performance in technical applications. In principle, molecular simulation can be used to predict the relevant properties of refrigerants and refrigerant blends, provided that adequate intermolecular potential functions ("force fields") are available. In our earlier work (Raabe, G.; Maginn, E. J., J. Phys. Chem. B2010, 114, 10133-10142), we introduced a transferable force field for fluoropropenes comprising the compounds 3,3,3-trifluoro-1-propene (HFO-1243zf), 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf), and hexafluoro-1-propene (HFO-1216). In this paper, we provide an extension of the force field model to the trans- and cis-1,3,3,3-tetrafluoro-1-propene (HFO-1234ze(E), HFO-1234ze) and the cis-1,2,3,3,3-pentafluoro-1-propene (HFO-1225ye(Z)) as well as revised simulation results for HFO-1216. We present Gibbs ensemble simulation results on the vapor pressures, saturated densities, and heats of vaporization of these compounds in comparison with experimental results. The simulation results show that the force field model enables reliable predictions of the properties of the different fluoropropenes and also reproduces well the differing vapor-liquid coexistence and vapor pressure curve of the cis- and trans-isomers of 1,3,3,3-tetrafluoro-1-propene, HFO-1234ze and HFO-1234ze(E). For these two isomers, we also present molecular dynamics simulation studies on their local structure. PMID:22519953
Quantized spin waves in antiferromagnetic Heisenberg chains.
Wieser, R; Vedmedenko, E Y; Wiesendanger, R
2008-10-24
The quantized stationary spin wave modes in one-dimensional antiferromagnetic spin chains with easy axis on-site anisotropy have been studied by means of Landau-Lifshitz-Gilbert spin dynamics. We demonstrate that the confined antiferromagnetic chains show a unique behavior having no equivalent, neither in ferromagnetism nor in acoustics. The discrete energy dispersion is split into two interpenetrating n and n' levels caused by the existence of two sublattices. The oscillations of individual sublattices as well as the standing wave pattern strongly depend on the boundary conditions. Particularly, acoustical and optical antiferromagnetic spin waves in chains with boundaries fixed (pinned) on different sublattices can be found, while an asymmetry of oscillations appears if the two pinned ends belong to the same sublattice. PMID:18999780
Cheating Heisenberg: Achieving certainty in wideband spectrography
NASA Astrophysics Data System (ADS)
Fulop, Sean
2003-10-01
The spectrographic analysis of sound has been with us some 58 years, and one of the key properties of the process is the trade-off in resolution between the time and frequency dimensions in the computed graph. While spectrography has greatly advanced the development of phonetics, the uncertainty principle has always been a source of frustration to phoneticians because so many of the interesting features of speech must be observed by computing Fourier spectra over very short time frames-i.e., using a ``wideband'' spectrogram. Since the uncertainty relation between time and frequency is unbreakable, the only option for improvement is to make a new kind of spectrogram that does not graph time and frequency. An algorithm is described and demonstrated which computes a new kind of spectrogram in which Fourier transform frequency is replaced by the channelized instantaneous frequency, and time is adjusted by the local group delay. The theory behind this procedure was clarified in Nelson [J. Acoust. Soc. Am. 110, 2575-2592 (2001)]. The resulting wideband spectrograms show dramatically improved resolution of speech features, which will be demonstrated with sample figures. It is thus suggested that phoneticians should be more interested in the instantaneous frequency spectrum than in the Fourier transform.
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.
Quantum Brownian motion model for the stock market
NASA Astrophysics Data System (ADS)
Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong
2016-06-01
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.
One-dimensional Kondo lattice model at quarter filling
NASA Astrophysics Data System (ADS)
Xavier, J. C.; Miranda, E.
2008-10-01
We revisit the problem of the quarter-filled one-dimensional Kondo lattice model, for which the existence of a dimerized phase and a nonzero charge gap had been reported by Xavier [Phys. Rev. Lett. 90, 247204 (2003)]. Recently, some objections were raised claiming that the system is neither dimerized nor has a charge gap. In the interest of clarifying this important issue, we show that these objections are based on results obtained under conditions in which the dimer order is artificially suppressed. We use the incontrovertible dimerized phase of the Majumdar-Ghosh point of the J1-J2 Heisenberg model as a paradigm with which to illustrate this artificial suppression. Finally, by means of extremely accurate density-matrix renormalization-group calculations, we show that the charge gap is indeed nonzero in the dimerized phase.
Technology Transfer Automated Retrieval System (TEKTRAN)
Saturated groundwater flow research on agricultural land in early times was mainly concerned with drainage of excessive rain. The key issue then was the spacing of drains or ditches to provide the efficient and effective removal, within a given time, of excessive water for a given soil. The focus wa...
ERIC Educational Resources Information Center
Currie-Knight, Kevin
2011-01-01
Jean-Jacques Rousseau (1712-1778) and Thomas Huxley (1852-1895) had different, but substantial, effects on the history of education. Rousseau's educational theories supplied the intellectual foundation for pedagogical progressivism. Huxley's educational writings helped to enlarge the scope of the British curriculum to include such things as…
Adelman, Jahred A.; Arguin, J.F.; Bellettini, G.; Brubaker, E.; Budagov, J.; Chlachidze, G.; Demortier, L.; Gibson, A.; Kim, S.; Kim, Y.K.; Maruyama, T.; Sato, K.; Shochet, M.; Sinervo, P.; Tomura, T.; Velev, G.; Xie, S.; Yang, U.K.; /Chicago U. /Toronto U. /INFN, Pisa /Dubna, JINR /Rockefeller U. /LBL, Berkeley /Tsukuba U. /Fermilab
2006-05-01
We report an updated measurement of the top quark mass in the lepton plus jets channel of t{bar t} events from p{bar p} collisions at {radical}s = 1.96 TeV. This measurement uses a dataset with integrated luminosity of 680 pb{sup -1}, containing 360 t{bar t} candidates separated into four subsamples. A top quark mass is reconstructed for each event by using energy and momentum constraints on the top quark pair decay products. We also employ the reconstructed mass of hadronic W boson decays W {yields} jj to constrain in situ the largest systematic uncertainty of the top quark mass measurement: the jet energy scale. Monte Carlo templates of the reconstructed top quark and W boson mass are produced as a function of the true top quark mass and the jet energy scale. The distribution of reconstructed top quark and W boson mass in the data are compared to the Monte Carlo templates using a likelihood fit to obtain: M{sub top} = 173.4 {+-} 2.8 GeV/c{sup 2}.
NASA Astrophysics Data System (ADS)
Lane, Kenneth D.
2011-04-01
I recount, in a personal way, the steps along the road that have led to the threshold of uncovering the dynamics of electroweak symmetry breaking. They began with a few theorists' profound dissatisfaction with the ``standard'' Higgs-boson description of this physics and have taken us to the enterprise of thousands - accelerator physicists, engineers, experimentalists and theorists - who designed, built and will now exploit the Large Hadron Collider at CERN.
Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
NASA Astrophysics Data System (ADS)
Batchelor, Murray T.; Foerster, Angela
2016-04-01
The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article we provide an introductory survey of the impact of Yang-Baxter integrable models on experiments in condensed matter physics and ultracold atoms. A number of prominent examples are covered, including the hard-hexagon model, the Heisenberg spin chain, the transverse quantum Ising chain, a spin ladder model, the Lieb-Liniger Bose gas, the Gaudin-Yang Fermi gas and the two-site Bose-Hubbard model. The review concludes by pointing to some other recent developments with promise for further progress.
Modeling and Reality in Early Twentieth-Century Physics
NASA Astrophysics Data System (ADS)
Seth, Suman
2011-04-01
Towards the end of 1913, Arnold Sommerfeld, Professor of theoretical physics at Munich University, sent a letter of congratulations to a young Niels Bohr. The Dane's now-classic trilogy of papers, which coupled Rutherford's conception of the atom with a ``planetary'' configuration of electrons, had just appeared. Sommerfeld saw the calculation of the Rydberg constant as a singular triumph and immediately spotted an opportunity to try to explain the Zeeman effect. Yet he also sounded a note of caution, confessing that he remained ``somewhat skeptical'' of atomic models in general. In this, of course, he was hardly alone. Bohr's atom was a particularly egregious example of a peculiar model, one requiring what even its creator considered ``horrid assumptions.'' Nonetheless, success bred conviction. Expanding upon Bohr's original ideas, Sommerfeld soon produced the so-called ``Bohr-Sommerfeld quantization conditions,'' using them to calculate a myriad of results. Experimental evidence, Sommerfeld argued in 1915, showed that quantised electron-paths ``correspond exactly to reality'' and possess ``real existence.'' This kind of realism would not, of course, last long. In 1925, Werner Heisenberg (earlier a student of Sommerfeld's) made scepticism about the details of the Bohr model into a methodological dictum, one later enshrined in the ``Copenhagen interpretation'' of quantum mechanics. This paper uses Sommerfeld's work from the turn of the twentieth century to the mid-1920s as a window onto a landscape involving multiple contestations over the legitimacy of atomic modelling. The surprise that greeted Heisenberg's and others' phenomenological insistences, we will see, can only be understood with reference to what should be considered a ``realist interlude'' in the history of twentieth century atomic physics, one inspired by the astonishing successes of Rutherford's and Bohr's imaginings.
Early atomic models - from mechanical to quantum (1904-1913)
NASA Astrophysics Data System (ADS)
Baily, C.
2013-01-01
A complete history of early atomic models would fill volumes, but a reasonably coherent tale of the path from mechanical atoms to the quantum can be told by focusing on the relevant work of three great contributors to atomic physics, in the critically important years between 1904 and 1913: J.J. Thomson, Ernest Rutherford and Niels Bohr. We first examine the origins of Thomson's mechanical atomic models, from his ethereal vortex atoms in the early 1880's, to the myriad "corpuscular" atoms he proposed following the discovery of the electron in 1897. Beyond qualitative predictions for the periodicity of the elements, the application of Thomson's atoms to problems in scattering and absorption led to quantitative predictions that were confirmed by experiments with high-velocity electrons traversing thin sheets of metal. Still, the much more massive and energetic α-particles being studied by Rutherford were better suited for exploring the interior of the atom, and careful measurements on the angular dependence of their scattering eventually allowed him to infer the existence of an atomic nucleus. Niels Bohr was particularly troubled by the radiative instability inherent to any mechanical atom, and succeeded in 1913 where others had failed in the prediction of emission spectra, by making two bold hypotheses that were in contradiction to the laws of classical physics, but necessary in order to account for experimental facts.
A constitutive model for Sn-Pb solder.
Neilsen, Michael K.; Vianco, Paul Thomas; Boyce, Brad Lee
2010-10-01
A unified creep plasticity damage (UCPD) model for Sn-Pb solder is developed in this paper. Stephens and Frear (1999) studied the creep behavior of near-eutectic 60Sn-40Pb solder subjected to low strain rates and found that the inelastic (creep and plastic) strain rate could be accurately described using a hyperbolic Sine function of the applied effective stress. A recently developed high-rate servo-hydraulic method was employed to characterize the temperature and strain-rate dependent stress-strain behavior of eutectic Sn-Pb solder over a wide range of strain rates (10{sup -4} to 10{sup 2} per second). The steady state inelastic strain rate data from these latest experiments were also accurately captured by the hyperbolic Sine equation developed by Stephens and Frear. Thus, this equation was used as the basis for the UCPD model for Sn-Pb solder developed in this paper. Stephens, J.J., and Frear, D.R., Metallurgical and Materials Transactions A, Volume 30A, pp. 1301-1313, May 1999.
Photochemical Modeling of the Distribution of C3H8 in the Atmosphere of Saturn
NASA Astrophysics Data System (ADS)
Edgington, S. G.; Simon-Miller, A.; Jennings, D.; Bjoraker, G.; Romani, P.; Achterberg, R.; Orton, G.; Flasar, M.; Cassini CIRS Team
2005-08-01
Cassini's Composite Infrared Spectrometer (CIRS) has measured the abundance of C2H2 and C3H8 (Propane) at several latitudes in the Southern hemisphere. An increase of radiance with latitude towards the pole has been observed, possibly implying a corresponding increase of C3H8. In an effort explain the observed distribution of both species, it is important to model the creation, destruction, and transport of these chemical species. Furthermore, since both molecules have overlapping absorption features in the same spectral region near 748 cm-1, such modeling will aid in refining derived abundances and separating temperature effects. The photochemistry model used in Edgington et al. (1998, 1999, 2000) to model simultaneously hydrocarbons, ammonia, and phosphine is updated and expanded to include paths relevant to the creation of C3H8. Destruction occurs through photolysis, while transport would tend to spread C3H8 from its source regions. With a series of exercises in 1- and 2- dimensions, we explore the extent to which photolysis, vertical, and/or meridional transport impacts the distribution of C2H2 and C3H8 with latitude. Thermal profiles derived from CIRS observations versus latitude are used as they have an impact on numerous reaction rates. We then compare these results with abundances derived from observations taken with the CIRS instrument. Edgington, S.G., West, R.A., Friedson, A.J., Atreya, S.K., 2000. A 2-D photochemical model with meridional circulation. Bull. American. Astron. Soc., 32, 1013. Edgington, S.G., S.K. Atreya, L.M. Trafton, J.J. Caldwell, R.F. Beebe, A.A. Simon, and R.A. West, 1999. Ammonia and eddy mixing variations in the southern hemisphere of Jupiter from HST Faint Object Spectrograph Observations. Icarus, 142, 342-357. Edgington, S.G., S.K. Atreya, L.M. Trafton, J.J. Caldwell, R.F. Beebe, A.A. Simon, R.A. West, and C. Barnet, 1998. On the latitude variation of ammonia, acetylene, and phosphine altitude profiles on Jupiter from HST Faint
Using Animations to Study the Formation of Gas Giant Planets via the Core Accretion Model
NASA Astrophysics Data System (ADS)
Hubickyj, O.; Lissauer, J. J.; Bodemheimer, P.; D'Angelo, G.
2009-12-01
Scripta 130, pp. 14024 Hubickyj, O., P. Bodenheimer, J. J. Lissauer 2005. Accretion of the gaseous envelope of Jupiter around a 5 10 Earth-mass core. Icarus, 179, 415--431. Kornet, K., P. Bodenheimer, M. Różyczka. and T. F. Stepinski 2005. Formation of giant planets in disks with different metallicities. Astron. Astrophys 430, 1133--1138. Lissauer, J. J., O. Hubickyj, G. D'Angelo, and P. Bodenheimer 2009. Models of Jupiter's growth incorporating thermal and hydrodynamic constraints. Icarus 199, 338--350. Pollack J. B., O. Hubickyj, P. Bodenheimer, J. J. Lissauer, M. Podolak, and Y. Greenzweig 1996. Formation of the giant planets by concurrent accretion of solids and gas. Icarus 67, 409--443. Valenti and Fischer 2008. Relationship between giant planet frequency and stellar metallicity. Physica Scripta 130, pp. 14003.
Ising-nematic order in the bilinear-biquadratic model for the iron pnictides
NASA Astrophysics Data System (ADS)
Bilbao Ergueta, Patricia; Nevidomskyy, Andriy H.
2015-10-01
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations even above the magnetic transition temperature TN, we study the spin dynamics within the frustrated Heisenberg model with biquadratic spin-spin exchange interactions. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the C4 symmetry even into the paramagnetic region TN
Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model
NASA Astrophysics Data System (ADS)
Eidelstein, Eitan; Moukouri, S.; Schiller, Avraham
2011-07-01
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.
An efficient basis for the modeling of doped and undoped S=1/2 antiferromagnet
NASA Astrophysics Data System (ADS)
Lau, Bayo; Berciu, Mona; Sawatzky, George A.
2012-02-01
We formulate an efficient numerical basis to model both doped and undoped S=12 Heisenberg antiferromagnet (AFM) with two-dimensional periodic boundary condition (2DPBC). Using a linear combination of Slater determinants with total-spin symmetries, a variational approach is developed to systematically and combinatorially decreases the Hilbert space of the problems, allowing the application of exact diagonalization to record-breaking system sizes. We can now model explicitly the wavefunction of an undoped 64-spin AFM square lattice with 2DPBC. For the doped scenarios, we solve a half-filled lattice with 32 coppers and 64 oxygens with one or two electrons removed. This allows, for the first time, a direct comparison of 32-unit-cell exact diagonalization between multi-band model and the t-J model, quantifying several oxygen-specific properties relevant to the lightly doped cuprate structures.
Joseph John Thomson's models of matter and radiation in the early 1890s.
Bordoni, Stefano
In the late nineteenth century, Joseph John Thomson moved away from Maxwell's specific theoretical models of matter and energy, even though he continued to rely on the general framework of Maxwell's electromagnetic theory. In his 1893 book, he accomplished the conceptual drift towards a discrete model for matter, electricity, and fields. In Thomson's model, energy was linked to tubes of force, in particular to the aether contained in them and surrounding them: the energy was the kinetic energy of aether, of both a rotational and translational kind. Starting from Maxwell's electromagnetic fields, namely stresses propagating through a continuous solid medium, Thomson arrived at a representation of fields as a sea of discrete units carrying energy and momentum. He tried to transform Maxwell's theory into a unified picture in which atomic models of matter stood beside atomic models of fields. In 1904 his interpretation of X-rays was based on the integration between two complementary features of electromagnetic radiation, the continuity and the discreteness, and on some kind of fibrous aether. In recent secondary literature, the problematic conceptual link between J. J. Thomson's theory and contemporary theories on electromagnetic radiation has been underestimated. On the contrary, in the first half of the twentieth century, some physicists inquired into that link, and a widespread debate emerged, misunderstandings included. PMID:25029824
Three-dimensional instantaneous dynamics modeling of present-day Aegean subduction
NASA Astrophysics Data System (ADS)
Glerum, Anne; Thieulot, Cedric; Pranger, Casper; van Hinsbergen, Douwe; Fraters, Menno; Spakman, Wim
2015-04-01
The Aegean region (Eastern Mediterranean) is exemplary of the interaction between crustal tectonics, plate motion, subduction and mantle flow: African subduction underneath the region has been continuous for at least the last 100 My, leading to about 2100-2500 km of subducted lithosphere residing in the mantle (van Hinsbergen et al., 2005). During this subduction, decoupled upper continental and oceanic crust accreted into a wedge of stacked nappes. In turn, these nappes have been significantly extended, predominantly during the last 25 My, due to the retreat of the African slab relative to Eurasia (van Hinsbergen and Schmid, 2012). As a first step to better understanding the coupling of the tectonic evolution of the crust and the underlying mantle dynamics, we are developing 3-D numerical models of the instantaneous dynamics of the present-day Aegean subduction system using the finite element code ASPECT (Kronbichler et al., 2012). The instantaneous models are set up with initial slab geometries derived from tomography and realistic plate boundary configurations and incorporate the major crustal weak zones of the overriding plate. Our modeling results in predictions of flow fields and stress, strain rate and rotation rate fields for the present-day tectonic setting of the Aegean region. By comparing our various model predictions to the widely available observations, such as focal mechanisms, GPS velocities and seismic anisotropy, we aim at an improved understanding of how mantle flow, subduction morphology and possibly slab segmentation, as well as the rheological behavior of the overriding plate, control present-day tectonic deformation. We expect to show preliminary results of this comparison. Kronbichler, M., Heister, T. and Bangerth, W. (2012), High Accuracy Mantle Convection Simulation through Modern Numerical Methods, Geophysical Journal International, 191, 12-29. Van Hinsbergen, D. J. J., Hafkenscheid, E., Spakman, W., Meulenkamp, J. E. and Wortel, R. (2005
Imagery and Synectics for Modeling Poetry Writing.
ERIC Educational Resources Information Center
Dykstra, Jeanne; Dykstra, Frank E.
Synectics is the use of thinking in metaphors, or figurative language in general, to see the familiar in unfamiliar ways or the unfamiliar in familiar ways. W.J.J. Gordon and his Cambridge Synectics Group isolated ways to think metaphorically by using artistic problem-solving mechanisms most people possess in their experiential background. This…
EPR pairing dynamics in Hubbard model with resonant U
Zhang, X. Z.; Song, Z.
2016-01-01
We study the dynamics of the collision between two fermions in Hubbard model with on-site interaction strength U. The exact solution shows that the scattering matrix for two-wavepacket collision is separable into two independent parts, operating on spatial and spin degrees of freedom, respectively. The S-matrix for spin configuration is equivalent to that of Heisenberg-type pulsed interaction with the strength depending on U and relative group velocity vr. This can be applied to create distant EPR pair, through a collision process for two fermions with opposite spins in the case of |vr/U| = 1, without the need for temporal control and measurement process. Multiple collision process for many particles is also discussed. PMID:26728282
Loth, E.; Tryggvason, G.; Tsuji, Y.; Elghobashi, S. E.; Crowe, Clayton T.; Berlemont, A.; Reeks, M.; Simonin, O.; Frank, Th; Onishi, Yasuo; Van Wachem, B.
2005-09-01
Slurry flows occur in many circumstances, including chemical manufacturing processes, pipeline transfer of coal, sand, and minerals; mud flows; and disposal of dredged materials. In this section we discuss slurry flow applications related to radioactive waste management. The Hanford tank waste solids and interstitial liquids will be mixed to form a slurry so it can be pumped out for retrieval and treatment. The waste is very complex chemically and physically. The ARIEL code is used to model the chemical interactions and fluid dynamics of the waste.
NASA Astrophysics Data System (ADS)
Dijkstra, P.; Fairbanks, D.; Miller, E.; Salpas, E.; Hagerty, S.
2013-12-01
Understanding the mechanisms regulating C cycling is hindered by our inability to directly observe and measure the biochemical processes of glycolysis, pentose phosphate pathway, and TCA cycle in intact and complex microbial communities. Position-specific 13C labeled metabolic tracer probing is proposed as a new way to study microbial community energy production, biosynthesis, C use efficiency (the proportion of substrate incorporated into microbial biomass), and enables the quantification of C fluxes through the central C metabolic network processes (Dijkstra et al 2011a,b). We determined the 13CO2 production from U-13C, 1-13C, 2-13C, 3-13C, 4-13C, 5-13C, and 6-13C labeled glucose and 1-13C and 2,3-13C pyruvate in parallel incubations in three soils along an elevation gradient. Qualitative and quantitative interpretation of the results indicate a high pentose phosphate pathway activity in soils. Agreement between modeled and measured CO2 production rates for the six C-atoms of 13C-labeled glucose indicate that the metabolic model used is appropriate for soil community processes, but that improvements can be made. These labeling and modeling techniques may improve our ability to analyze the biochemistry and (eco)physiology of intact microbial communities. Dijkstra, P., Blankinship, J.C., Selmants, P.C., Hart, S.C., Koch, G.W., Schwartz, E., Hungate, B.A., 2011a. Probing C flux patterns of soil microbial metabolic networks using parallel position-specific tracer labeling. Soil Biology & Biochemistry 43, 126-132. Dijkstra, P., Dalder, J.J., Selmants, P.C., Hart, S.C., Koch, G.W., Schwartz, E., Hungate, B.A., 2011b. Modeling soil metabolic processes using isotopologue pairs of position-specific 13C-labeled glucose and pyruvate. Soil Biology & Biochemistry 43, 1848-1857.
Multiscale modeling of ultrafast element-specific magnetization dynamics of ferromagnetic alloys
NASA Astrophysics Data System (ADS)
Hinzke, D.; Atxitia, U.; Carva, K.; Nieves, P.; Chubykalo-Fesenko, O.; Oppeneer, P. M.; Nowak, U.
2015-08-01
A hierarchical multiscale approach to model the magnetization dynamics of ferromagnetic random alloys is presented. First-principles calculations of the Heisenberg exchange integrals are linked to atomistic spin models based upon the stochastic Landau-Lifshitz-Gilbert (LLG) equation to calculate temperature-dependent parameters (e.g., effective exchange interactions, damping parameters). These parameters are subsequently used in the Landau-Lifshitz-Bloch (LLB) model for multisublattice magnets to calculate numerically and analytically the ultrafast demagnetization times. The developed multiscale method is applied here to FeNi (permalloy) as well as to copper-doped FeNi alloys. We find that after an ultrafast heat pulse the Ni sublattice demagnetizes faster than the Fe sublattice for the here-studied FeNi-based alloys.
Modeling of the magnetic free energy of self-diffusion in bcc Fe
NASA Astrophysics Data System (ADS)
Sandberg, N.; Chang, Z.; Messina, L.; Olsson, P.; Korzhavyi, P.
2015-11-01
A first-principles based approach to calculating self-diffusion rates in bcc Fe is discussed with particular focus on the magnetic free energy associated with diffusion activation. First, the enthalpies and entropies of vacancy formation and migration in ferromagnetic bcc Fe are calculated from standard density functional theory methods in combination with transition state theory. Next, the shift in diffusion activation energy when going from the ferromagnetic to the paramagnetic state is estimated by averaging over random spin states. Classical and quantum mechanical Monte Carlo simulations within the Heisenberg model are used to study the effect of spin disordering on the vacancy formation and migration free energy. Finally, a quasiempirical model of the magnetic contribution to the diffusion activation free energy is applied in order to connect the current first-principles results to experimental data. The importance of the zero-point magnon energy in modeling of diffusion in bcc Fe is stressed.
NASA Technical Reports Server (NTRS)
Batchelor, David; Zukor, Dorothy (Technical Monitor)
2001-01-01
New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approximately Planck's constant/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only Planck's constant and c.
Diboson excesses in an anomaly free leptophobic left-right model
NASA Astrophysics Data System (ADS)
Das, Kasinath; Li, Tianjun; Nandi, S.; Rai, Santosh Kumar
2016-01-01
The resonant excesses around 2 TeV reported by the ATLAS Collaboration can be explained in the left-right model, and the tight constraints from lepton plus missing energy searches can be evaded if the S U (2 )R gauge symmetry is leptophobic. We, for the first time, propose an anomaly- free leptophobic left-right model with gauge symmetry S U (3 )C×S U (2 )L×S U (2 )R×U (1 )X , where the SM leptons are singlets under S U (2 )R . The gauge anomalies are cancelled by introducing extra vectorlike quarks. The mass of the Z' gauge boson, which cannot be leptophobic, is assumed to be around or above 2.5 TeV so that the constraint on the dilepton final state can be avoided. Moreover, we find that the W'→W Z channel cannot explain the ATLAS diboson excess due to the tension with the constraint on the W'→j j decay mode. We solve this problem by considering the mixings between the SM quarks and vectorlike quarks. We show explicitly that the ATLAS diboson excess can be explained in the viable parameter space of our model, which is consistent with all the current experimental constraints.
A model of the ionosphere of Saturn's rings and its implications
NASA Astrophysics Data System (ADS)
Luhmann, J. G.; Johnson, R. E.; Tokar, R. L.; Ledvina, S. A.; Cravens, T. E.
2006-04-01
The detection of cold O2+ and O + ions in the vicinity of Saturn's rings during the Cassini Orbiter orbit insertion confirmed expectations that the rings would have a water product atmosphere and ionosphere. These observations prompted a new look at their origin and nature by Johnson et al. [Johnson, R.E., Luhmann, J.G., Tokar, R.L., Bouhram, M., Berthelier, J.J., Sittler, E.C., Cooper, J.F., Hill, T.W., Crary, F.J., Young, D.T., 2006. Icarus 180, 393-402], but also raised questions about the ionosphere's spatial distribution and fate that inspired the ionospheric model described in this report. Here a test particle model with some Monte Carlo aspects is used to consider the behavior of the O2+ and O + ions produced in the atmosphere of Saturn's rings. Key features of these calculations include the Johnson et al. description of the production of the ring atmosphere, and the effects of the offset dipole magnetic field of Saturn. The results suggest that the latter should produce some possibly observable asymmetries in both the inner ring ionosphere and the precipitation of ring ions into the atmosphere of Saturn. Further in situ observations of the rings are not currently planned, but remote sensing instruments on Cassini may provide future observational tests of the model.