The scaling behavior of logarithmic fidelity in quantum phase transition in LMG model

TL;DR

This paper investigates how logarithmic fidelity scales with system size in quantum phase transitions within the LMG model, revealing phase-dependent behavior and critical point singularities.

Contribution

It provides a detailed analysis of the size scaling of logarithmic fidelity in the LMG model, highlighting differences between classical and quantum fidelities and their phase dependence.

Findings

Logarithmic fidelity scales as N in the symmetry-broken phase.

Logarithmic fidelity is size-independent in the polarized phase.

Critical point exhibits singular behavior in fidelity scaling.

Abstract

In this paper, we explore the differences between classical logarithmic fidelity and quantum fidelity. The classical logarithmic fidelity is found to be always extensive while the quantum one manifests distinct size dependence in different phases. Illustrated by the anisotropic Lipkin-Meshkov-Glick model, we found numerically and analytically that the logarithmic fidelity scales like N in the symmetry-broken phase and scales like N^0 in the polarized phase. The singular behavior around the critical point is also investigated.