Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis
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Wang, Q., & Pérez-Bernal, F. (2021). Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis. Physical Review E, 104(3), 034119.[https://doi.org/10.1103/PhysRevE.104.034119]
SponsorshipNational Natural Science Foundation of China (NSFC) 11805165; Zhe-jiang Provincial Nature Science Foundation LY20A050001; Slovenian Research Agency - Slovenia J1-9112 P1-0306; European Commission SOMM17/6105/UGR; EDER/MINECO UNHU-15CE-2848; Consejeria de Conocimiento, Investigacion y Universidad, Junta de An-dalucia UHU-1262561; Ministerio de Ciencia, Innovacion y Universidades COOPB20364
Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.