Theory of Out-of-Time-Ordered Transport

TL;DR

This paper develops an effective field theory to describe late-time out-of-time-order correlators in quantum many-body systems, revealing universal behaviors, connections to transport phenomena, and sensitivity to novel transport parameters.

Contribution

It introduces a generalized EFT for OTOCs that unifies their late-time behavior with conventional hydrodynamics and identifies new transport parameters accessible via specific OTOC combinations.

Findings

OTOCs exhibit universal late-time power-law behavior.

Many OTOCs are determined by standard transport data.

Certain OTOC combinations reveal new transport parameters.

Abstract

We construct an effective field theory (EFT) that captures the universal behavior of out-of-time-order correlators (OTOCs) at late times in generic quantum many-body systems with conservation laws. The EFT hinges on a generalization of the strong-to-weak spontaneous symmetry breaking pattern adapted to out-of-time-order observables, and reduces to conventional fluctuating hydrodynamics when time-ordered observables are probed. We use the EFT to explain different power-law behavior observed in OTOCs at late times, and show that many OTOCs are entirely fixed by conventional transport data. Nevertheless, we show that a specific combination of OTOCs is sensitive to novel transport parameters, not visible in regular time-ordered correlators. We test our predictions in Hamiltonian and Floquet spin chains in one dimension.