Quantum information spreading in generalised dual-unitary circuits

TL;DR

This paper investigates quantum information dynamics in generalized dual-unitary circuits, revealing maximal operator spreading speed, exact entanglement growth characterization, and a novel entanglement membrane expression.

Contribution

It extends dual-unitary circuit analysis to a broader class, providing exact entanglement dynamics and revealing differences in entanglement velocity.

Findings

Operators spread at maximal speed (light speed).

Entanglement growth is exactly characterized for certain initial states.

Entanglement velocity is generally less than one.

Abstract

We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalises the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a restricted subspace. First, we show that local operators spread at the speed of light as in dual-unitary circuits, i.e., the butterfly velocity takes the maximal value allowed by the geometry of the circuit. Then, we prove that the entanglement spreading can still be characterised exactly for a family of compatible initial states (in fact, for an extension of the compatible family of dual-unitary circuits) and that the asymptotic entanglement slope is again independent on the R\'enyi index. Remarkably, however, we find that the entanglement velocity is generically smaller than one. We use these properties to find a closed-form expression for the entanglement membrane in these circuits.