Fidelity approach to quantum phase transitions

TL;DR

This paper reviews the quantum fidelity approach to quantum phase transitions, providing a systematic framework and applications to specific models, aiming to enhance understanding of quantum critical phenomena.

Contribution

It offers a comprehensive pedagogical review and unifies various results on fidelity in quantum phase transitions into a systematic theoretical framework.

Findings

Explicit application to the transverse-field Ising model

Application to the Lipkin-Meshkov-Glick model

Survey of different fidelity approaches in many-body systems

Abstract

We review briefly the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick model, are introduced at the graduate-student level. In addition, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.