The Lipkin-Meshkov-Glick model from the perspective of the SU(1,1) Richardson-Gaudin models

36th Symposium on Nuclear Physics

Lerma-H, Sergio^1 ; Dukelsky, Jorge^2

Departamento de Física, Facultad de Física e Inteligencia Artificial, Universidad Veracruzana, Lomas del Estadio s/n, C.P. 91000, Xalapa, Veracruz, Mexico^1

Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Spain^2

关键词: Approximation methods;    Electrostatic problems;    Equilibrium positions;    Lipkin-Meshkov-Glick model;    Model Hamiltonians;    Model parameters;    Spectral parameters;    Two dimensional spaces;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/492/1/012013/pdf
DOI  :  10.1088/1742-6596/492/1/012013

来源: IOP

【 摘 要 】

Originally introduced in nuclear physics as a numerical laboratory to test different many-body approximation methods, the Lipkin-Meshkov-Glick (LMG) model has received much attention as a simple enough but non-trivial model with many interesting features for areas of physics beyond the nuclear one. In this contribution we look at the LMG model as a particular example of an SU(1,1) Richardson-Gaudin model. The characteristics of the model are analyzed in terms of the behavior of the spectral-parameters or pairons which determine both eigenvalues and eigenfunctions of the model Hamiltonian. The problem of finding these pairons is mathematically equivalent to obtain the equilibrium positions of a set of electric charges moving in a two dimensional space. The electrostatic problems for the different regions of the model parameter space are discussed and linked to the different energy density of states already identified in the LMG spectrum.