The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model

TL;DR

This paper introduces a novel method analyzing Majorana polynomial roots to compute the spectrum of the Lipkin-Meshkov-Glick model in the thermodynamical limit, revealing a complex phase structure beyond the ground state analysis.

Contribution

It presents a new approach based on polynomial root analysis to explore the spectral properties of the model in the thermodynamic limit.

Findings

Identification of four distinct regions in parameter space

Discovery of a richer phase structure than ground state analysis

Spectral analysis revealing complex phase behavior

Abstract

A method based on the analyzis of the Majorana polynomial roots is introduced to compute the spectrum of the Lipkin-Meshkov-Glick model in the thermodynamical limit. A rich structure made of four qualitatively different regions is revealed in the parameter space whereas the ground state study only distinguishes between two phases.