Proposal for many-body quantum chaos detection
arxiv(2024)
Abstract
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.
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