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

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 Rényi 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.

9 (6+3) pages; v2 as appears in Phys. Rev. Lett

References in corpus (9)

• Thermalization and its mechanism for generic isolated quantum systems
• Critical properties of the measurement-induced transition in random quantum circuits
• Matrix Product States for dynamical simulation of infinite chains
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Scrambling in Random Unitary Circuits: Exact Results
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Connecting Entanglement in Time and Space: Improving the Folding Algorithm
• Exact matrix product decay modes of a boundary driven cellular automaton

Cited by in corpus (7)

• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• A Yang-Baxter integrable cellular automaton with a four site update rule
• BBGKY Hierarchy and Generalised Hydrodynamics
• Integrability breaking in the Rule 54 cellular automaton
• Reversible Cellular Automata as Integrable Interactions Round-a-Face: Deterministic, Stochastic, and Quantized
• Entanglement dynamics of thermofield double states in integrable models
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps