The entanglement membrane in chaotic many-body systems

TL;DR

This paper extends the concept of the entanglement membrane from random unitary circuits to more realistic chaotic systems, providing a new framework for understanding entanglement dynamics and out-of-time-order correlators.

Contribution

It introduces an effective pairing framework for entanglement membranes in non-random models, enabling analysis of entanglement and chaos in realistic quantum systems.

Findings

Defined a consistent entanglement line tension in Floquet spin chains.

Identified qualitative differences in line tension between generic and dual-unitary circuits.

Developed an efficient numerical algorithm for entanglement line tension in 1+1D.

Abstract

In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an ``entanglement membrane'' in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This provides a framework for applying ideas of coarse-graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane, and that there are qualitative differences in this tension between generic models and ``dual-unitary'' circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to non-random Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in 1+1D.