Exact quench dynamics of the Floquet quantum East model at the deterministic point

TL;DR

This paper provides an exact analysis of the nonequilibrium thermalization and entanglement growth in a specific Floquet quantum spin chain model at a deterministic point, revealing precise bounds and scaling behaviors.

Contribution

It offers an exact solution for the thermalization dynamics and entanglement growth in the Floquet quantum East model at the deterministic point, a novel analytical achievement.

Findings

Entanglement grows at half the maximum speed allowed by locality.

Classical initial states exhibit a quarter of the maximal entanglement speed.

Thermalization to infinite temperature occurs in a time proportional to the block size.

Abstract

We study the nonequilibrium dynamics of the Floquet quantum East model (a Trotterized version of the kinetically constrained quantum East spin chain) at its "deterministic point", where evolution is defined in terms of CNOT permutation gates. We solve exactly the thermalization dynamics for a broad class of initial product states by means of "space evolution". We prove: (i) the entanglement of a block of spins grows at most at one-half the maximal speed allowed by locality (i.e., half the speed of dual-unitary circuits); (ii) if the block of spins is initially prepared in a classical configuration, speed of entanglement is a quarter of the maximum; (iii) thermalization to the infinite temperature state is reached exactly in a time that scales with the size of the block.