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

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.

Integrable matrix models in discrete space-time

“…[28]), it remains obscure at this moment if this has any implications on the structure of dynamical correlations in these matrix models, or possibly even for the observed anomalous transport behavior. We wish to stress here that this type of self-duality differs fundamentally from the so-called dual-unitarity found recently in the context of quantum circuits [99,127] where correlations are locked to the light-rays. In our models, dynamical correlations functions (averaged in a flat invariant measure) fill the entire causal cone in a non-trivial fashion.…”

“…Furthermore, correlations do not only propagate with the unit speed as e.g. in the dual-unitary models [99]. In Section 3 we carry out numerical simulations to explicitly demonstrate this fact.…”

Kardar–Parisi–Zhang Physics in Integrable Rotationally Symmetric Dynamics on Discrete Space–Time Lattice

“…We note that space-time duality has been discussed in space-time continuous integrable field theories, where existence of a unique space dynamics can be connected to a Lax zero-curvature condition [24]. However, in discrete space-time setting it is not clear if space-time (self-)duality is connected to integrability, in particular, since in quantum systems it has been found even in maximally chaotic dynamics [25,26,27].…”

Dual Approach to the Spectral Form Factor

“…Based on Refs. [10,11] that study the self-dual situation it can be already expected that they show an interesting behavior in the short-time regime of the order of the duration between a few kicks.…”

“…These two properties lead to the characterization of that system as maximally chaotic. Finally, this system shows special spatio-temporal structures of correlation functions [11]. In Ref.…”