Structural Stability Hypothesis of Dual Unitary Quantum Chaos
arxiv(2024)
摘要
Having spectral correlations that, over small enough energy scales, are
described by random matrix theory is regarded as the most general defining
feature of quantum chaotic systems as it applies in the many-body setting and
away from any semiclassical limit. Although this property is extremely
difficult to prove analytically for generic many-body systems, a rigorous proof
has been achieved for dual-unitary circuits – a special class of local quantum
circuits that remain unitary upon swapping space and time. Here we consider the
fate of this property when moving from dual-unitary to generic quantum circuits
focussing on the spectral form factor, i.e., the Fourier transform of
the two-point correlation. We begin with a numerical survey that, in agreement
with previous studies, suggests that there exists a finite region in parameter
space where dual-unitary physics is stable and spectral correlations are still
described by random matrix theory, although up to a maximal quasienergy scale.
To explain these findings, we develop a perturbative expansion: it recovers the
random matrix theory predictions, provided the terms occurring in perturbation
theory obey a relatively simple set of assumptions. We then provide numerical
evidence and a heuristic analytical argument supporting these assumptions.
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