Many-body quantum chaos and dual-unitarity round-a-face

Abstract

We propose a new type of locally interacting quantum circuits—quantum cellular automata—that are generated by unitary interactions round-a-face (IRF). Specifically, we discuss a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension d [DUIRF(d)], which generate unitary evolutions both in space and time directions of an extended 1+1 dimensional lattice. We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite-dimensional completely positive trace preserving unital maps in complete analogy to recently studied circuits made of dual-unitary brick gates (DUBGs). The simplest non-vanishing local correlation functions in dual-unitary IRF circuits are shown to involve observables non-trivially supported on two neighboring sites. We completely characterize the ten-dimensional manifold of DUIRF(2) for qubits (d=2) and provide, for d=3,4,…,7, empirical estimates of its dimensionality based on numerically determined dimensions of tangent spaces at an ensemble of random instances of dual-unitary IRF gates. In parallel, we apply the same algorithm to determine dimDUBG(d) and show that they are of similar order though systematically larger than dimDUIRF(d) for d=2,3,…,7. It is remarkable that both sets have a rather complex topology for d≥3 in the sense that the dimension of the tangent space varies among different randomly generated points of the set. Finally, we provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions d≠d′ residing at even/odd lattice sites.

Temporal entanglement, quasiparticles and the role of interactions

“…Instead, it is related to the so-called temporal entanglement (TE) [12], which is naturally understood as the entanglement generated along a space-time rotated direction [6]. This approach has recently received renewed interest in connection to the study of space-time dualities in Floquet kicked Ising chains [13,14] and dual-unitary quantum circuits [15], see [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In addition, similar ideas motivated related constructions exploiting space-time rotation in generic quantum-circuit dynamics [30][31][32][33][34][35].…”

A Yang-Baxter integrable cellular automaton with a four site update rule

“…As explained in Section 4 it can be considered an integrable Trotterization of the "folded XXZ model", and in this respect it is a 3-site (or 4-site) generalization of the work [24]. Our model is also similar to the dual unitary gate models of [21,22,23] and the dual unitary round-a-face models of [33]. These models apply one control bit (dual unitary gate models) or two control bits (dual unitary round-a-face models) for the action of a one site unitary.…”

Construction and the ergodicity properties of dual unitary quantum circuits

“…Various types of block diagonal constructions (or direct sums) appeared in [6,16,43]. The basic idea is to consider subspaces which are kept invariant in the diagonal direction.…”