Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry

TL;DR

This paper develops a quantum field theory framework for the X-cube fracton model, capturing its topological features and degeneracy, and introduces a novel approach that incorporates geometry and matter coupling.

Contribution

It presents the first non-topological quantum field theory description of the X-cube model, highlighting invariance under a subgroup of the conformal group and the role of geometry in degeneracy.

Findings

Field theory reproduces braiding statistics and degeneracy

Spatial curvature induces stable ground state degeneracy

Formalism applicable to other fracton theories

Abstract

We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant (i.e. symmetric) under continuous spacetime transformations. However, the theory is instead invariant under a certain subgroup of the conformal group. We describe how braiding statistics and ground state degeneracy are reproduced by the field theory, and how the the X-cube Hamiltonian and field theory can be minimally coupled to matter fields. We also show that even on a manifold with trivial topology, spatial curvature can induce a ground state degeneracy that is stable to arbitrary local perturbations! Our formalism may allow for the description of other fracton field theories, where the only necessary input is an equation of motion for a charge density.