Localization with random time-periodic quantum circuits

TL;DR

This paper investigates how random, time-periodic quantum circuits induce localization or thermalization in spin chains, providing analytical and numerical insights into the transition between these phases.

Contribution

It introduces a new numerical method to analyze quantum circuits and demonstrates the conditions under which localization or thermalization occurs in such systems.

Findings

Haar-distributed unitaries lead to full depolarization and thermalization.

A tunable coupling strength reveals a many-body localization transition.

Gaussian circuits exhibit localization in the covariance matrix, unlike homogeneous systems.

Abstract

We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with the same random instances. We obtain analytical results for arbitrary local Hilbert space dimension d: On a single site, average time evolution acts as a depolarising channel. In the spin 1/2 (d=2) case, this is further quantified numerically. For that, we develop a new numerical method that reduces complexity by an exponential factor. Haar-distributed unitaries lead to full depolarization after many timesteps, i.e. local thermalization. A unitary probability distribution with tunable coupling strength allows us to observe a many-body localization transition. In addition to a spin chain under a unitary circuit, we consider the analogous problem with Gaussian circuits. We can make stronger statements about the entire covariance matrix instead of single sites only, and find that the dynamics is localising. For a random time evolution operator homogeneous in space, however, the system delocalizes.