Emergent fermionic gauge theory and foliated fracton order in the Chamon model

TL;DR

This paper reveals that the Chamon model exhibits an emergent fermionic gauge theory coupled with a fractonic SPT state and hosts 4-foliated fracton order, advancing understanding of fracton phases and gauge theories.

Contribution

It demonstrates the emergence of a fermionic gauge theory and foliated fracton order in the Chamon model, providing new insights into fracton topological phases.

Findings

Emergent fermionic gauge theory coupled to SPT state

Host of 4-foliated fracton order

Exfoliation of 2D toric codes from the bulk

Abstract

The Chamon model is an exactly solvable spin Hamiltonian exhibiting nontrivial fracton order. In this work, we dissect two distinct aspects of the model. First, we show that it exhibits an emergent fractonic gauge theory coupled to a fermionic subsystem symmetry-protected topological state under four stacks of $\mathbb{Z}_2$ planar symmetries. Second, we show that the Chamon model hosts 4-foliated fracton order by describing an entanglement renormalization group transformation that exfoliates four separate stacks of 2D toric codes from the bulk system.