Quasi Many-body Localization in Translation Invariant Systems

TL;DR

This paper investigates quasi-many-body localization in translation-invariant systems, revealing a long-lived pre-thermal state with slow entanglement growth and eventual spin transport decay, challenging the necessity of disorder for localization.

Contribution

It introduces the concept of quasi-many-body localization in translation-invariant systems and characterizes its dynamical properties and underlying length scale.

Findings

Slow entanglement growth at intermediate times

Finite-time decay of spin polarization independent of system size

Identification of a length scale controlling spin transport and susceptibility

Abstract

It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in the context of a one-dimensional spin ladder. At intermediate time scales, we find slow growth of entanglement entropy consistent with the phenomenology of many-body localization. However, at longer times, all finite wavelength spin polarizations decay in a finite time, independent of system size. We identify a single length scale which parametrically controls both the eventual spin transport times and the divergence of the susceptibility to spin glass ordering. We dub this long pre-thermal dynamical behavior, intermediate between full localization and diffusion, quasi-many body localization.