Fidelity approach to quantum phase transitions

Details Fidelity approach to quantum phase transitions Fidelity approach to quantum phase transitions

2008-11-19

arxiv.org/abs/0811.3127v1

Int. J. Mod. Phys. B 24, 4371(2010)

Physics

Quantum Physics

41 pages, 31 figures. We apologize if we omit acknowledging your relevant works. Do tell. An updated version with clearer figu

Scientific paper

10.1142/S0217979210056335

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.

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