Fractonic topological phases from coupled wires

TL;DR

This paper explores three-dimensional fractonic topological phases using coupled wire models, revealing new types of excitations, surface states, and a unique bulk-boundary correspondence beyond traditional topological theories.

Contribution

It introduces coupled wire constructions for fractonic phases, demonstrating both gapped and gapless states with novel excitations and boundary phenomena.

Findings

Fractonic excitations are mobile along wires but restricted transversely.

Models exhibit infinite-order fusion structures, unlike known fracton models.

Surface states are described by infinite-component Luttinger liquids with orientation-dependent properties.

Abstract

In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the 2D coupled wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a new type of bulk-boundary correspondence unique to fracton phases.