scholarly journals The Yangian relations of Heisenberg spin chain model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guijiao Du ◽  
Kang Xue ◽  
Chengcheng Zhou
Keyword(s):  
Spin Chain ◽  
Particle System ◽  
Energy Levels ◽  
Xy Model ◽  
Chain Model ◽  
Xxz Model ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Spin Chain Model ◽  
Xxx Model

AbstractIn this paper, we investigate the Yangian relations of Heisenberg spin chain systems. Firstly, we consider the closed XXZ spin chain model, through the Heisenberg spin XXZ model, we found the Hamiltonians for one kind system of three adjacent partial particles interaction systems. The model’s constitution rules of energy levels and energy states which expand from the few-particle system to multi-particle system have good regularity. In this system, we found Yangian’s law and illustrate it through graphs. Secondly, we further consider the closed XXZ spin chain’s generalization of other three neighboring particles interaction systems from few-particle system to multi-particle system. Finally, we also discussed the laws of the three adjacent particles system of some models, they are the XXZ model with twist boundary condition, the open XXZ spin chain model and the XXZ model containing the next neighbor. In addition, not only XXZ model, XXX model, XY model and Ising model, but the relevant laws of spin-1 systems of these models were also discussed, they have similar rules to the XXZ model. Through calculation and research, the eigensystems of these models all have good Yangian and constitution laws.

ADIABATIC TRANSPORT PROPERTIES AND BERRY’S PHASE IN HEISENBERG-ISING RING

1991 ◽  
Vol 05 (03) ◽  
pp. 497-507 ◽  
Author(s):  
V.E. KOREPIN ◽  
A.C.T. WU
Keyword(s):  
Boundary Conditions ◽  
Transport Properties ◽  
Effective Charge ◽  
Spin Chain ◽  
Energy Levels ◽  
Adiabatic Process ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain

In a recent paper, B. Sutherland and B.S. Shastry have constructed an adiabatic process for the Heisenberg spin chain (spin ½) with respect to a change of boundary conditions. In this paper we calculate Berry’s phase for this process. We also evaluate the dependence of energy levels on boundary conditions which permits us to calculate the effective charge-carrying mass.

scholarly journals Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

Open Physics ◽  
2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Grzegorz Kwiatkowski ◽  
Sergey Leble
Keyword(s):  
Spin Chain ◽  
Functional Integral ◽  
Quasiclassical Approximation ◽  
Quantum Corrections ◽  
Classical Solutions ◽  
Chain Model ◽  
Model Approximation ◽  
Heisenberg Spin Chain ◽  
Spin Chain Model ◽  
The One

AbstractThe Heisenberg spin chain is considered in ϕ 4 model approximation. Quantum corrections to classical solutions of the one-dimensional ϕ 4 model within the correspondent physics are evaluated with account of rest d-1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in a quasiclassical approximation. The results are applied to appropriate conditions of the spin chain model and its dynamics, for which elementary solutions, energy and the quantum corrections are calculated.

Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

2015 ◽  
Vol 13 (03) ◽  
pp. 1550017
Author(s):  
Bo Liu ◽  
Kang Xue ◽  
Gangcheng Wang ◽  
Ying Liu ◽  
Chunfang Sun
Keyword(s):  
Spin Chain ◽  
Three Dimensional ◽  
Quantum Spin ◽  
Chain Model ◽  
Superposition State ◽  
Quantum Spin Chain ◽  
Xxz Model ◽  
Spin Chain Model ◽  
Bmw Algebra ◽  
Spin Chain Models

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.

Thermal correlations and entropic uncertainty in a two-spin system under DM and KSEA interactions

2021 ◽  
pp. 2150209
Author(s):  
Youssef Khedif ◽  
Saeed Haddadi ◽  
Mohammad Reza Pourkarimi ◽  
Mohammed Daoud
Keyword(s):  
Magnetic Field ◽  
Quantum Information Processing ◽  
Quantum Correlations ◽  
Quantum Nonlocality ◽  
Chain Model ◽  
Spin Orbit ◽  
Heisenberg Spin ◽  
System Parameters ◽  
Heisenberg Spin Chain ◽  
Spin Chain Model

In this paper, the thermal quantum correlations along with the thermal entropic uncertainty in a two neighboring XYZ Heisenberg spin-1/2 particles subjected to a transverse external magnetic field with the interplay of both antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony are investigated. The quantum consonance and uncertainty-induced quantum nonlocality as well as the entropic uncertainty with quantum memory for the considered system are specified and the thermal behaviors of them in terms of the system parameters are examined. The expected decrease of quantum correlations for higher absolute temperatures is confirmed while the inflation of the uncertainty is generated. Moreover, we show that the stronger spin-spin and spin-orbit exchange couplings can enhance the thermal quantum correlations and suppress the uncertainty. Accordingly, our remarks are expected to be beneficent in illustrating the dynamical quantum correlations and entropy-based uncertainty in a general Heisenberg spin-chain model and thus would be useful for practical quantum information processing.

scholarly journals Billiards on constant curvature spaces and generating functions for systems with constraints

2017 ◽  
Vol 44 (1) ◽  
pp. 103-114 ◽  
Author(s):  
Bozidar Jovanovic
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Generating Functions ◽  
Spin Chain ◽  
Spin Model ◽  
Chain Model ◽  
Heisenberg Spin ◽  
Lobachevsky Space ◽  
Spin Chain Model ◽  
Magnetic Spin

In this note we consider a method of generating functions for systems with constraints and, as an example, we prove that the billiard mappings for billiards on the Euclidean space, sphere, and the Lobachevsky space are sympletic. Further, by taking a quadratic generating function we get the skew-hodograph mapping introduced by Moser and Veselov, which relates the ellipsoidal billiards in the Euclidean space with the Heisenberg magnetic spin chain model on a sphere. We define analogous mapping for the ellipsoidal billiard on the Lobachevsky space. It relates the billiard with the Heisenberg spin model on the light-like cone in the Lorentz-Poincare-Minkowski space.

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