Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions

TL;DR

This paper derives exact, non-perturbative dynamical correlation functions for a broad class of dual-unitary quantum lattice models in 1+1 dimensions, revealing diverse classes of correlation behavior.

Contribution

It provides the first explicit calculation of all dynamical correlations in dual-unitary circuits, including a classification of circuit types based on correlation dynamics.

Findings

Exact correlation functions for dual-unitary circuits

Classification of circuits into non-interacting, ergodic, and mixed classes

Identification of non-ergodic, interacting classes

Abstract

We consider a class of quantum lattice models in $1+1$ dimensions represented as local quantum circuits that enjoy a particular "dual-unitarity" property. In essence, this property ensures that both the evolution "in time" and that "in space" are given in terms of unitary transfer matrices. We show that for this class of circuits, generically non-integrable, one can compute explicitly all dynamical correlations of local observables. Our result is exact, non-pertubative, and holds for any dimension $d$ of the local Hilbert space. In the minimal case of qubits ($d = 2$) we also present a classification of all dual-unitary circuits which allows us to single out a number of distinct classes for the behaviour of the dynamical correlations. We find "non-interacting" classes, where all correlations are preserved, the ergodic and mixing one, where all correlations decay, and, interestingly, also classes that are are both interacting and non-ergodic.