Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension

TL;DR

This paper develops methods to construct dual-unitary quantum circuits with controllable ergodic or non-ergodic behavior across any local Hilbert space dimension, providing analytical insights into thermalization and prethermalization phenomena.

Contribution

It introduces a systematic way to design dual-unitary circuits with tunable ergodicity and derives analytical results for their thermalization properties.

Findings

Constructed classes of dual-unitary circuits with arbitrary ergodicity levels.

Derived analytical results for thermalization to Gibbs and generalized Gibbs ensembles.

Showed how perturbations induce prethermalization in non-ergodic circuits.

Abstract

Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unitarity, leading to the appearance of prethermalization plateaux for local observables.