Bifurcating entanglement-renormalization group flows of fracton stabilizer models

TL;DR

This paper studies the entanglement-renormalization group flows of 3D fracton topological models, revealing bifurcation behavior and proposing a new classification framework for these phases.

Contribution

It introduces the concept of bifurcated equivalence for fracton phases and generalizes related notions, advancing the understanding of 3D topological stabilizer models.

Findings

Fracton models bifurcate under entanglement renormalization.

Bifurcation often leads to at least one copy of the original model.

Proposes conjectures for classifying 3D topological stabilizer models.

Abstract

We investigate the entanglement-renormalization group flows of translation-invariant topological stabilizer models in three dimensions. Fracton models are observed to bifurcate under entanglement renormalization, generically returning at least one copy of the original model. Based on this behavior we formulate the notion of bifurcated equivalence for fracton phases, generalizing foliated fracton equivalence. The notion of quotient superselection sectors is also generalized accordingly. We calculate bifurcating entanglement-renormalization group flows for a wide range of examples and, based on those results, propose conjectures regarding the classification of translation-invariant topological stabilizer models in three dimensions.