论文标题
广义的Lipkin-Meshkov-Glick型号和修改的代数Bethe Ansatz
The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz
论文作者
论文摘要
我们表明，在外部磁场中，Lipkin-Meshkov-Glick $ 2N $ -Fermion模型是一种特殊的gaudin型模型的特殊情况，该模型对应于与一个非对称椭圆形$ r $ r $ -matrix的限制案例，以及沿着一个Axis的外部磁场。我们根据对应于相同的$ r $ -Matrix但任意外部磁场的Gaudin型模型，提出了基于Gaudin型模型的Lipkin-Meshkov-Glick-Glick fermion模型的完全可分化的概括。该模型与经典Zhukovsky-Volterra陀螺仪的量化相吻合。我们通过修改的代数贝尔斯ansatz对相应的量子哈密顿量对角线化。我们明确地为小费米数$ n = 1,2 $的情况明确求解相应的伯特型方程。
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 $N=1,2$.
