Exotic Field Theories for (Hybrid) Fracton Phases from Imposing Constraints in Foliated Field Theory

TL;DR

This paper establishes a connection between foliated quantum theories and exotic field theories to better describe fracton phases, providing new models and demonstrating their equivalence with known theories.

Contribution

It explicitly constructs a map from foliated quantum theory to exotic field theory, including new models for hybrid fracton phases and demonstrating their equivalence.

Findings

Recovered the equivalence between foliated and exotic fractonic BF theories.

Established the equivalence of toric code layers and anisotropic models to foliated BF theories.

Derived new exotic field theories for hybrid fracton phases.

Abstract

Fracton phases of matter are gapped phases of matter that, by dint of their sensitivity to UV data, demand non-standard quantum field theories to describe them in the IR. Two such approaches are foliated quantum theory and exotic field theory. In this paper, we explicitly construct a map from one to the other and work out several examples. In particular, we recover the equivalence between the foliated and exotic fractonic BF theories recently demonstrated at the level of operator correspondence. We also demonstrate the equivalence of toric code layers and the anisotropic model with lineons and planons to the foliated BF theory with one and two foliations, respectively. Finally, we derive new exotic field theories that provide simple descriptions of hybrid fracton phases from foliated field theries known to do so. Our results both provide new examples of exotic field theories and pave the way toward their systematic construction from foliated field theories.