Fracton phases via exotic higher-form symmetry-breaking

TL;DR

This paper explores the mechanisms of p-string condensation in fracton phases through higher-form symmetry, providing a unified framework for understanding these exotic phases beyond specific lattice models.

Contribution

It introduces a general perspective on higher-form symmetry in lattice models and applies it to analyze fracton phases like the X-cube model and scalar charge theories.

Findings

Identification of foliated 1-form symmetry in the X-cube model

Discovery of framed 1-form symmetry in scalar charge theory

Clarification of p-string condensation via higher-form symmetry

Abstract

We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. We also give a general discussion on interpreting p-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.