Facilitated quantum cellular automata as simple models with nonthermal eigenstates and dynamics

TL;DR

This paper introduces simple facilitated quantum spin models with Floquet dynamics that can be classically simulated, exhibiting nonthermal eigenstates and integrability properties, with some eigenstates showing strong entanglement features.

Contribution

The paper presents a new class of facilitated quantum cellular automata models with explicit constructions of conserved quantities and analysis of their entanglement properties.

Findings

Models can be classically simulated and eigenstates explicitly constructed.

Some models are integrable with conserved densities.

Eigenstates can be strongly subthermal and disentangled due to symmetry.

Abstract

We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a Floquet unitary. The dynamics of the models we discuss can be classically simulated, and their eigenstates classically constructed (although they are highly entangled). We consider a variety of models in both one and two dimensions, involving Clifford gates and Toffoli gates. For some of these models, we explicitly construct conserved densities; thus these models are "integrable." The other models do not seem to be integrable; yet, for some system sizes and boundary conditions, their eigenstate entanglement is strongly subthermal. Some of the models have exponentially many eigenstates in which one or more sites are "disentangled" from the rest of the system, as a consequence of reflection symmetry.