Localization from superselection rules in translation invariant systems

TL;DR

This paper demonstrates that in a translation invariant 3D spin system, most finite energy states are localized due to an emergent superselection rule, without the need for disorder, and identifies local integrals of motion.

Contribution

It reveals a mechanism for localization in translation invariant systems via superselection rules and characterizes the associated local integrals of motion.

Findings

Most finite energy states are localized below a critical perturbation strength.

Energy remains concentrated around defects for near-exponential times.

The phenomenon extends to systems with immobile topological excitations.

Abstract

We study a translation invariant spin model in a three-dimensional regular lattice, called the cubic code model, in the presence of arbitrary extensive perturbations. Below a critical perturbation strength, we show that most states with finite energy are localized; the overwhelming majority of such states have energy concentrated around a finite number of defects, and remain so for a time that is near-exponential in the distance between the defects. This phenomenon is due to an emergent superselection rule and does not require any disorder. An extensive number of local integrals of motion for these finite energy sectors are identified as well. Our analysis extends more generally to systems with immobile topological excitations.