Emergence of many-body quantum chaos via spontaneous breaking of unitarity

Journal Article · Mon Apr 18 00:00:00 EDT 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.105.l140202· OSTI ID:1979783

Liao, Yunxiang ^[1]; Galitski, Victor ^[2]

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1. Univ. of Maryland, College Park, MD (United States); OSTI
2. Univ. of Maryland, College Park, MD (United States)

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as K(η,t)=$$\langle$$|Tr exp(-ηH+itH)|²$$\rangle$$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the “unitary” η = 0 case is different from the η → 0^± limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

• Research Organization: Univ. of Maryland, College Park, MD (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0001911
• OSTI ID: 1979783
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 14 Vol. 105; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
Quantum chaos
nonlinear sigma model
path-integral methods
random matrix theory