Fractional excitations in foliated fracton phases

TL;DR

This paper introduces a new framework for characterizing fractional excitations in foliated fracton phases, accounting for their unique mobility constraints and exotic braiding, and demonstrates this with the X-cube models.

Contribution

It proposes a universal characterization of fractional excitations in foliated fracton phases, considering equivalence up to 2D quasiparticle additions, and establishes phase relations between models.

Findings

Defined fractional excitations up to 2D quasiparticle attachments.

Provided a universal characterization of foliated fracton order.

Established equivalence between X-cube and semionic X-cube models.

Abstract

Fractional excitations in fracton models exhibit novel features not present in conventional topological phases: their mobility is constrained, there are an infinitude of types, and they bear an exotic sense of 'braiding'. Hence, they require a new framework for proper characterization. Based on our definition of foliated fracton phases in which equivalence between models includes the possibility of adding layers of gapped 2D states, we propose to characterize fractional excitations in these phases up to the addition of quasiparticles with 2D mobility. That is, two quasiparticles differing by a set of quasiparticles that move along 2D planes are considered to be equivalent; likewise, 'braiding' statistics are measured in a way that is insensitive to the attachment of 2D quasiparticles. The fractional excitation types and statistics defined in this way provide a universal characterization of the underlying foliated fracton order which can subsequently be used to establish phase relations. We demonstrate as an example the equivalence between the X-cube model and the semionic X-cube model both in terms of fractional excitations and through an exact mapping.