Continuum mechanics of entanglement in noisy interacting fermion chains

TL;DR

This paper develops a continuum theoretical framework to describe information scrambling and entanglement dynamics in noisy, interacting Majorana fermion chains, providing exact results in certain limits and revealing novel phenomena like entanglement membrane unbinding.

Contribution

It introduces a semiclassical continuum approach for entanglement and operator spreading in fermionic chains, capturing weak interaction regimes and novel bound state phenomena.

Findings

Exact entanglement membrane results in weak interaction limit

Identification of a large crossover lengthscale enabling continuum limit

Discovery of entanglement membrane unbinding near butterfly velocity

Abstract

We develop an effective continuum description for information scrambling in a chain of randomly interacting Majorana fermions. The approach is based on the semiclassical treatment of the path integral for an effective spin chain that describes "two-replica" observables such as the entanglement purity and the OTOC. This formalism gives exact results for the entanglement membrane and for operator spreading in the limit of weak interactions. In this limit there is a large crossover lengthscale between free and interacting behavior, and this large lengthscale allows for a continuum limit and a controlled saddle-point calculation. The formalism is also somewhat different from that known from random unitary circuits. The entanglement membrane emerges as a kind of bound state of two travelling waves, and shows an interesting unbinding phenomenon as the velocity of the entanglement membrane approaches the butterfly velocity.