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

Abstract

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 $K(\eta ,t)=⟨|\mathrm{Tr}\exp (-\eta H+itH){|}^2⟩$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the "unitary" $\eta =0$ case is different from the $\eta \to 0^{\pm }$ 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 non-interacting case, and gives rise to a non-trivial 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.

7+26 pages, 2+2 figures

References in corpus (16)

• Thermalization and its mechanism for generic isolated quantum systems
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Chaos, Complexity, and Random Matrices
• Late time physics of holographic quantum chaos
• Local pairing of Feynman histories in many-body Floquet models
• Many-body level statistics of single-particle quantum chaos
• An exponential ramp in the quadratic Sachdev-Ye-Kitaev model
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• Many-body delocalisation as symmetry breaking
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
• Spectral Lyapunov exponents in chaotic and localized many-body quantum systems
• A minimal model of many body localization
• From operator statistics to wormholes
• Quantum ergodicity in the many-body localization problem
• Correlated Disorder in the SYK${}_2$ model
• Non-Markovian dephasing of disordered, quasi-one-dimensional fermion systems

Cited by in corpus (12)

• Many-body quantum chaos and emergence of Ginibre ensemble
• Many-body quantum chaos in stroboscopically-driven cold atoms
• Dynamical quantum ergodicity from energy level statistics
• Spectral form factor in a minimal bosonic model of many-body quantum chaos
• Unitarity breaking in self-averaging spectral form factors
• Universal Dephasing Mechanism of Many-Body Quantum Chaos
• Exact universal bounds on quantum dynamics and fast scrambling
• Replica Symmetry Breaking for the Integrable Two-Site Sachdev-Ye-Kitaev Model
• Many-body quantum chaos in mixtures of multiple species
• Effective field theory of random quantum circuits
• Higher spin wormholes from modular bootstrap
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes