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

2016/12/14 by Ching-Yee Leung, Ho-Man Kwok, Leung, Ching-Yee +5
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1612.04690

openalex publication_date 2016/12/14 · openalex created_date 2017/02/17 · openalex updated_date 2026/07/28

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 N⁰ in the polarized phase. The singular behavior around the critical point is also investigated.

Related

• Fidelity and quantum phase transitions
• Singularities in ground state fidelity and quantum phase transitions for the Kitaev model
• Singularities in fidelity surfaces for quantum phase transitions: a geometric perspective
• Universality and Scaling Properties of Correlation Functions Near a Quantum Phase Transition
• High-order fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction