Chaos detection; Correlation holes; Form factors; Level correlation; Level statistics; Many body; Quantum chaos; Random matrices theory; Spectral correlation; Survival probabilities; Physics and Astronomy (all); Physics - Statistical Mechanics; Quantum Physics
Résumé :
[en] In this work, the term "quantum chaos"refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using, e.g., the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers.
Disciplines :
Physique
Auteur, co-auteur :
Das, Adway Kumar ; Department of Physics, University of Connecticut, Storrs, United States ; Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, India
Cianci, Cameron ; Department of Physics, University of Connecticut, Storrs, United States ; Mirion Technologies (Canberra) Inc., Meriden, United States
Cabral, Delmar G. A.; Department of Chemistry, Yale University, New Haven, United States
Zarate-Herrada, David A. ; Institut of Physics, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
Pinney, Patrick ; Department of Physics, University of Connecticut, Storrs, United States
Pilatowsky-Cameo, Saúl ; Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, United States
MATSOUKAS, Stylianos Apollonas ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Adolfo DEL CAMPO ECHEVARRIA
Batista, Victor S.; Department of Chemistry, Yale University, New Haven, United States
DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Torres-Herrera, E. Jonathan ; Institut of Physics, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
Santos, Lea F. ; Department of Physics, University of Connecticut, Storrs, United States
Fulbright Association Consejo Nacional de Humanidades, Ciencias y Tecnologías National Science Foundation Center for Cultural Innovation Department of Forestry and Natural Resources, Purdue University Vicerrectoría de Investigación y Estudios de Posgrado, Benemérita Universidad Autónoma de Puebla Kavli Institute for Theoretical Physics, University of California, Santa Barbara Nehru Luxembourg National Research Fund Fulbright Association Consejo Nacional de Humanidades, Ciencias y Tecnologías National Science Foundation Center for Cultural Innovation Department of Forestry and Natural Resources, Purdue University Vicerrectoría de Investigación y Estudios de Posgrado, Benemérita Universidad Autónoma de Puebla Kavli Institute for Theoretical Physics, University of California, Santa Barbara Nehru Luxembourg National Research Fund
Subventionnement (détails) :
A.K.D. is supported by the Fulbright-Nehru Grant No. 2879/FNDR/2023-2024. D.A.Z.-H. and E.J.T.-H. are supported by CONAHCYT through Project No. CF-2023-I-1748. D.C. and V.S.B. are funded by the NSF CCI grant (Award No. 2124511). A.d.C. is supported by the Luxembourg National Research Fund (FNR), Grant Reference [17132054]. E.J.T.-H. is grateful for financial support from VIEP-BUAP, Project No. 00165-2023. D.A.Z.-H. and E.J.T.-H. are grateful to LNS-BUAP for their supercomputing facility. L.F.S. is supported by the NSF Grant No. DMR-1936006. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).
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The spectrum of this model for (Equation presented) presents a combination of GSE-like statistics, in the case of short-range correlations, and GOE-like statistics for long-range correlations. It has been shown analytically with full random matrices that the minimum value of (Equation presented) and the saturation value (Equation presented), where (Equation presented) for GOE, GUE, and GSE, respectively [38].
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