Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton

TL;DR

This paper provides an exact analytical description of the thermalization dynamics in the Rule 54 quantum cellular automaton, revealing non-Markovian behavior and interaction effects in a solvable many-body quantum system.

Contribution

It offers the first exact microscopic solution for the full thermalization process in a non-trivial quantum cellular automaton.

Findings

Analytic formulas for local observable evolution

Demonstration of non-Markovian dynamics in Rule 54

Identification of interaction-induced dressing effects

Abstract

We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54". For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulae for the evolution of local observables and R\'enyi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical non-equilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.