2008/11/19 by Shi-Jian Gu, SHI-JIAN GU · 592 citations
Physics and Astronomy · #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1142/s0217979210056335
published in International Journal of Modern Physics B 24(23), 4371-4458 (World Scientific Pub Co Pte Ltd) · 41 pages, 31 figures. We apologize if we omit acknowledging your relevant works. Do tell. An updated version with clearer figures can be found at: http://www.phy.cuhk.edu.hk/~sjgu/fidelitynote.pdf
arxiv created 2008/11/19 · crossref issued 2010/09/20 · crossref published 2010/09/20 · crossref published-print 2010/09/20 · crossref created 2010/12/09 · arxiv updated 2010/12/14 · crossref published-online 2012/05/02 · crossref deposited 2021/11/15 · crossref indexed 2026/08/06
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.