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.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.

arXiv:1412.3999Physics of Particles and NucleiMay 1, 20152 citations

Study on the correlation properties in the three-qubit spin chain of Heisenberg XYZ model

Hakimeh Jaghouri

Quantum Information ProcessingJan 12, 20242 citations

The Yangian relations of Heisenberg spin chain model

Guijiao Du, Kang Xue, Chengcheng Zhou

In 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.In 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.

Scientific ReportsJul 16, 20211 citation

Correlation functions of the XXZ Heisenberg spin- chain in a magnetic field

N Kitanine, Jean Michel Maillet, V. Terras

arXiv:math-ph/9907019Nuclear Physics BFeb 1, 2000342 citations

Correlation amplitude for the S=12 XXZ spin chain in the critical region: Numerical renormalization-group study of an open chain

Takashi Hikihara, Akira Furusaki

The density-matrix renormalization-group technique is used to calculate the spin-correlation functions $〈{S}_{j}^{x}{S}_{k}^{x}〉$ and $〈{S}_{j}^{z}{S}_{k}^{z}〉$ of the one-dimensional $S=\frac{1}{2}$ $\mathrm{XXZ}$ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.The density-matrix renormalization-group technique is used to calculate the spin-correlation functions $〈{S}_{j}^{x}{S}_{k}^{x}〉$ and $〈{S}_{j}^{z}{S}_{k}^{z}〉$ of the one-dimensional $S=\frac{1}{2}$ $\mathrm{XXZ}$ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.

arXiv:cond-mat/9803159Physical review. B, Condensed matterJul 1, 199870 citations

Phase Transitions and Quantum Correlations in Heisenberg XXZ Spin Chains

Mounaim Hamdoune, Mohammed Daoud A

International Journal of Theoretical PhysicsAug 8, 20260 citations

The density-matrix renormalization-group technique is used to calculate the spin-correlation functions

〈{S}_{j}^{x}{S}_{k}^{x}〉

and

〈{S}_{j}^{z}{S}_{k}^{z}〉

of the one-dimensional

S=\frac{1}{2}

\mathrm{XXZ}

model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.