广义Lipkin-Meshkov-Glick模型及其修正代数beatz

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-10-10 DOI:10.3842/SIGMA.2022.074

T. Skrypnyk

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引用次数: 1

摘要

我们证明了Lipkin-Meshkov-Glick 2n -费米子模型是外磁场中单自旋高丁型模型的特殊情况，对应于非偏对称椭圆r矩阵的极限情况和沿一轴方向的外磁场。我们提出了一种精确可解的Lipkin-Meshkov-Glick费米子模型的推广方法，该模型基于对应于相同r矩阵但任意外磁场的gaudin型模型。该模型与经典朱可夫斯基-沃尔泰拉陀螺的量子化一致。利用改进的代数Bethe ansatz对角化了相应的量子哈密顿量。对于小费米子数N=1,2的情况，我们显式地求解了相应的bethe型方程。

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The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz

We show that the Lipkin-Meshkov-Glick 2N-fermion model is a particular case of one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of non-skew-symmetric elliptic r-matrix and to an external magnetic field directed along one axis. We propose an exactly-solvable generalization of the Lipkin-Meshkov-Glick fermion model based on the Gaudin-type model corresponding to the same r-matrix but arbitrary external magnetic field. This model coincides with the quantization of the classical Zhukovsky-Volterra gyrostat. We diagonalize the corresponding quantum Hamiltonian by means of the modified algebraic Bethe ansatz. We explicitly solve the corresponding Bethe-type equations for the case of small fermion number N=1,2.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.