Universal Dephasing Mechanism of Many-Body Quantum Chaos

TL;DR

This paper reveals a universal dephasing mechanism that underpins the emergence of many-body quantum chaos, linking spectral form factor behavior to interactions and trajectory interference in quantum systems.

Contribution

It introduces a microscopic explanation for the transition to quantum chaos via dephasing, supported by analysis of the SYK model family.

Findings

Dephasing disrupts trajectory interference, leading to the linear spectral form factor ramp.

In the non-interacting limit, dephasing vanishes, resulting in exponential growth of the spectral form factor.

Chaotic regimes exhibit dephasing that suppresses exponential ramp and induces level correlations.

Abstract

Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of "time", t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-$t$ ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex $\mbox{SYK}_2+\mbox{SYK}_2^2$ model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the non-interacting $\mbox{SYK}_2$ model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the non-interacting theory and induces correlations between many-body levels.