Exact results on the dynamics of the stochastic Floquet-East model

TL;DR

This paper introduces a stochastic version of the Floquet-East model, proving a phase transition between active and inactive states and analyzing fluctuations, with implications for kinetically constrained models and tensor network methods.

Contribution

It provides the first exact analysis of a stochastic Floquet-East model, revealing a phase transition and fluctuation scaling, and connects discrete and continuous-time East models.

Findings

Existence of a large deviation phase transition between active and inactive phases.

Finite time and size scaling of fluctuations shows dynamical hydrophobicity.

Results apply to continuous-time East model via Trotter limit.

Abstract

We introduce a stochastic generalisation of the classical deterministic Floquet-East model, a discrete circuit with the same kinetic constraint as the East model of glasses. We prove exactly that, in the limit of long time and large size, this model has a large deviation phase transition between active and inactive dynamical phases. We also compute the finite time and size scaling of general space-time fluctuations, which for the case of inactive regions gives rise to dynamical hydrophobicity. We also discuss how, through the Trotter limit, these exact results also hold for the continuous-time East model, thus proving long-standing observations in kinetically constrained models. Our results here illustrate the applicability of exact tensor network methods for solving problems in many-body stochastic systems.