Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
Volume 24, Issue 23, Pages 4371-4458Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217979210056335
Keywords
Fidelity; fidelity susceptibility; quantum phase transitions
Funding
- Research Grants Council of HKSAR, China [CUHK 400807, CUHK 402107, CUHK 401108, HKUST3/CRF/09]
- CUHK [2060392]
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We review 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. Besides, 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.
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