Exact Thermalization Dynamics in the Rule 54 Quantum Cellular Automaton

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 formulas for the evolution of local observables and Renyi 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 nonequilibrium 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.

Automated summary

In this study, the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 was examined, revealing the full thermalization dynamics at a microscopic level using simple quantum channels for low-entangled initial states. Analytic formulas for the evolution of local observables and Renyi entropies were provided, showing that Rule 54 does not behave as a simple Markovian bath and exhibits nonequilibrium features of interacting integrable many-body quantum systems. This study offers a rare example where the entire thermalization dynamics can be exactly solved at the microscopic level.