4 February 2021 Thu 4 pm

< Previous

Next >

Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are "as random as a coin-toss". Dual-unitary circuits have been recently introduced as solvable models of many-body nonintegrable quantum chaotic systems having a hierarchy of ergodic properties. We extend this to include the apex of a putative quantum ergodic hierarchy which is Bernoulli, in the sense that correlations of single and two-particle observables vanish at space-time separated points. We derive a condition based on the entangling power ep(U) of the basic two-particle unitary building block, U, of the circuit, that guarantees mixing, and when maximized, corresponds to Bernoulli circuits. Additionally we show, both analytically and numerically, how local-averaging over single-particle unitaries leads to an identification of the average mixing rate as being determined solely by the entangling power ep(U). The same considerations extend to disordered dual-unitary circuits as well. Finally we provide several, both analytical and numerical, ways to construct dual-unitary operators covering the entire possible range of entangling power. We construct a coupled quantum cat map which is dual-unitary for all local dimensions and a 2-unitary or perfect tensor for odd local dimensions, and can be used to build Bernoulli circuits. These constructions and results pave the way for a systematic extension of quantities studied in the dual-unitary circuits as well as provide natural generalizations to the non-dual cases.

Based on https://arxiv.org/abs/2101.04580