Gapped Interfaces in Fracton Models and Foliated Fields

TL;DR

This paper explores the structure of gapped interfaces in 3+1d fracton phases using foliated gauge theories, revealing new boundary types and dualities that deepen understanding of fracton topological order.

Contribution

It introduces novel gapped interfaces, including decorated boundaries and duality interfaces, expanding the classification of fracton phase boundaries and their symmetries.

Findings

Discovered a gapped boundary where electric lineons become magnetic lineons.

Constructed a Kramers-Wannier-duality type interface between X-cube and toric code.

Identified an electromagnetic duality interface exchanging electric and magnetic lineons.

Abstract

This work investigates the gapped interfaces of 3+1d fracton phases of matter using foliated gauge theories and lattice models. We analyze the gapped boundaries and gapped interfaces in X cube model, and the gapped interfaces between the X-cube model and the toric code. The gapped interfaces are either "undecorated" or "decorated", where the "decorated" interfaces have additional Chern-Simons like actions for foliated gauge fields. We discover many new gapped boundaries and interfaces, such as (1) a gapped boundary for X-cube model where the electric lineons orthogonal to the interface become the magnetic lineons, the latter are the composite of magnetic planons; (2) a Kramers-Wannier-duality type gapped interface between the X-cube model and the toric code model from gauging planar subsystem one-form symmetry; and (3) an electromagnetic duality interface in the X-cube model that exchanges the electric and magnetic lineons.