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

Autor:	Skrypnyk, Taras
Rok vydání:	2022
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics
Zdroj:	SIGMA 18 (2022), 074, 18 pages
Druh dokumentu:	Working Paper
DOI:	10.3842/SIGMA.2022.074
Popis:	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 $N=1,2$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.04454 Zobrazit plný text záznamu View this record from Arxiv