Universal entanglement signatures of foliated fracton phases

TL;DR

This paper introduces universal entanglement signatures for foliated fracton phases, extending topological entanglement entropy concepts to these exotic phases and demonstrating their invariance and non-zero values.

Contribution

It proposes multi-partite entanglement measures as universal invariants for foliated fracton phases, generalizing topological entanglement entropy.

Findings

Entanglement measures are non-zero constants in non-trivial phases.

Universal properties remain invariant under phase-preserving transformations.

The approach extends topological entanglement entropy to fracton phases.

Abstract

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In a previous work, we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.