Quantum phase transitions in networks of Lipkin-Meshkov-Glick models

TL;DR

This paper investigates quantum phase transitions in networks of Lipkin-Meshkov-Glick models, revealing different phases and degeneracies through mean-field analysis and quantum corrections, with analytical results for ring topology networks.

Contribution

It provides a detailed analysis of quantum critical behavior in LMG networks, highlighting the effects of anisotropic coupling and topology on ground state degeneracy and ordering.

Findings

Weak coupling leads to paramagnetic phase with exponentially degenerate ground state.

Strong coupling results in a twofold degenerate ground state with magnetic order.

Analytical solutions are derived for ring topology networks.

Abstract

We study the quantum critical behavior of networks consisting of Lipkin-Meshkov-Glick models with an anisotropic ferromagnetic coupling. We focus on the low-energy properties of the system within a mean-field approach and the quantum corrections around the mean-field solution. Our results show that the weak-coupling regime corresponds to the paramagnetic phase when the local field dominates the dynamics, but the local anisotropy leads to the existence of an exponentially-degenerate ground state. In the strong-coupling regime, the ground state is twofold degenerate and possesses long-range magnetic ordering. Analytical results for a network with the ring topology are obtained.