Roughening Transition in Quantum Circuits

TL;DR

This paper investigates a phase transition in the entanglement dynamics of quantum circuits, modeling entanglement as a membrane in a random environment, revealing a disorder-induced roughening transition and novel scaling behaviors.

Contribution

It introduces a membrane-based framework for entanglement in quantum circuits and uncovers a new disorder-driven roughening transition with unique scaling properties.

Findings

Identifies a disorder-induced roughening transition in a (3+1)D Clifford circuit.

Develops a scaling theory for tilted entanglement membranes.

Discovers a crossover to a new critical tilted regime.

Abstract

We explore a roughening phase transition that occurs in the entanglement dynamics of certain quantum circuits. Viewing entanglement as the free energy of a membrane in a circuit-defined random environment, there is a competition between membrane smoothing due to lattice pinning and roughening due to disorder in the circuit. In particular, we investigate the randomness-induced roughening transition of the entanglement membrane in a (3+1)-dimensional Clifford circuit model, by calculating the entanglement entropy for various bipartitions. We further construct a scaling theory for membranes tilted away from lattice planes, uncovering new scaling forms and a crossover to a previously unexplored critical "tilted regime".