Logarithmic entanglement growth from disorder-free localization in the two-leg compass ladder

TL;DR

This paper demonstrates that disorder-free localized systems exhibit logarithmic entanglement growth and temperature-dependent correlation decay, resembling many-body localization phenomena.

Contribution

It reveals how finite-temperature dynamics in quasi-1D orbital models mimic disorder-induced localization without actual disorder.

Findings

Logarithmic entanglement growth observed

Correlation functions decay with temperature-dependent exponents

Models provide experimentally accessible disorder-free localization signatures

Abstract

We explore the finite-temperature dynamics of the quasi-1D orbital compass and plaquette Ising models. We map these systems onto a model of free fermions coupled to strictly localized spin-1/2 degrees of freedom. At finite temperature, the localized degrees of freedom act as emergent disorder and localize the fermions. Although the model can be analyzed using free-fermion techniques, it has dynamical signatures in common with typical many-body localized systems: Starting from generic initial states, entanglement grows logarithmically; in addition, equilibrium dynamical correlation functions decay with an exponent that varies continuously with temperature and model parameters. These quasi-1D models offer an experimentally realizable setting in which natural dynamical probes show signatures of disorder-free many-body localization.