Fracton Topological Order, Generalized Lattice Gauge Theory and Duality

TL;DR

This paper introduces a generalized lattice gauge theory framework to describe fracton topological phases, revealing a duality with certain spin systems and providing mathematical tools for their identification and potential material realization.

Contribution

It develops a new theoretical approach to characterize fracton phases using algebraic geometry and duality, expanding the understanding of topological matter.

Findings

Established a duality between fracton order and lower-dimensional spin symmetries

Provided a mathematical framework using algebraic geometry for fracton phases

Suggested pathways for material realization of fracton topological phases

Abstract

We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical toolset for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.