Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits

TL;DR

This paper investigates entanglement growth in many-body quantum systems using random unitary circuits, revealing a connection to membrane roughening phenomena in higher dimensions through extensive numerical simulations.

Contribution

It introduces a novel characterization of entanglement growth via membrane roughening exponents in $(d+1)$-dimensional elastic media, based on extensive Clifford circuit simulations.

Findings

Entanglement growth properties are linked to membrane roughening exponents.

Numerical simulations in dimensions 1 to 4 support the membrane analogy.

Clifford circuits effectively model entanglement fluctuations.

Abstract

Understanding the nature of entanglement growth in many-body systems is one of the fundamental questions in quantum physics. Here, we study this problem by characterizing the entanglement fluctuations and distribution of $(d+1)$ qubit lattice evolved under a random unitary circuit. Focusing on Clifford gates, we perform extensive numerical simulations of random circuits in $1\le d\le 4$ dimensions. Our findings demonstrate that properties of growth of bipartite entanglement entropy are characterized by the roughening exponents of a $d$-dimensional membrane in a $(d+1)$ elastic medium.