Lattice Clifford fractons and their Chern-Simons-like theory

TL;DR

This paper constructs lattice fracton models in arbitrary odd spatial dimensions using Clifford algebra representations and develops their effective Chern-Simons-like theories, revealing new insights into fractonic behavior and topological properties.

Contribution

It introduces a general method to build lattice fracton models in odd dimensions using Dirac matrices and derives their effective topological field theories.

Findings

Fracton models constructed in odd dimensions with Clifford algebra

Effective Chern-Simons-like theories with hierarchical quantum Hall features

Conservation of gauge charges in sub-dimensional manifolds

Abstract

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.