Quantum information spreading in generalised dual-unitary circuits

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.