Analysis of quantum phase transition in some different Curie-Weiss models: a unified approach

TL;DR

This paper introduces a unified method for analyzing quantum phase transitions across various Curie-Weiss models by transforming their Hamiltonians into a classical form using $SU(2)$ operators, applicable to multiple models.

Contribution

It presents a general scheme that simplifies the analysis of quantum phase transitions in different models through Hamiltonian balancing and $SU(2)$ operator representation.

Findings

Successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.

Provides a common framework for analyzing diverse quantum phase transitions.

Facilitates comparison and understanding of different models' critical behavior.

Abstract

A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum Hamiltonian by an appropriate factor, rewriting the Hamiltonian in terms of $SU(2)$ operators only, and obtention of a classical Hamiltonian. $SU(2)$ operators are obtained from creation and annihilation operators as linear combinations in the case of fermions and as an inverse Holstein-Primakoff transformation in the case of bosons. This scheme is successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.