Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Q.W. acknowledges support from the National Science Foundation of China under Grant No. 11805165, Zhejiang Provincial Nature Science Foundation under Grant No. LY20A050001, and Slovenian Research Agency (ARRS) under the Grants No. J1-9112 and No. P1-0306. This work has also been partially supported by the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), Ref. No. SOMM17/6105/UGR and by the Ministerio de Ciencia, Innovación y Universidades (Ref. No. COOPB20364). F.P.-B. also thanks support from Project No. UHU-1262561. Computing resources supporting this work were partly provide by the CEAFMC and Universidad de Huelva High Performance Computer (HPC@UHU) located in the Campus Universitario el Carmen and funded by FEDER/MINECO Project No. UNHU-15CE-2848.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.National Natural Science Foundation of China (NSFC) 11805165Zhe-jiang Provincial Nature Science Foundation LY20A050001Slovenian Research Agency - Slovenia J1-9112 P1-0306European Commission SOMM17/6105/UGREDER/MINECO UNHU-15CE-2848Consejeria de Conocimiento, Investigacion y Universidad, Junta de An-dalucia UHU-1262561Ministerio de Ciencia, Innovacion y Universidades COOPB2036