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Universal entanglement signatures of foliated fracton phases

by Wilbur Shirley, Kevin Slagle, Xie Chen

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Submission summary

As Contributors: Wilbur Shirley · Kevin Slagle
Arxiv Link: (pdf)
Date accepted: 2019-01-17
Date submitted: 2019-01-10 01:00
Submitted by: Shirley, Wilbur
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


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.

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Published as SciPost Phys. 6, 015 (2019)

Author comments upon resubmission

We thank the referees for their reports and Referee #2 for their constructive comments.

List of changes

We have made the following changes in accordance with Referee #2's suggestions.

1) to improve the accessibility of the paper to a broader audience, the authors could perhaps spend a few words to explain what they mean by the double arrow "adiabatic evolution" in Eq.(1)

We have added the following sentence to explain what is meant by adiabatic evolution: "Here, adiabatic evolution refers to a smooth deformation of the Hamiltonian that preserves the energy gap, i.e. one that does not pass through an intervening gapless phase."

2) proofreading for typos: "the the" and "fracon". Missing period at the end of Eq.(5).

These typos have been fixed.

3) I think that the von Neumann entropy in Eq.(6) has the wrong sign

This error has been corrected.

4) at the end of Sec.3.1, the authors cite Ref.32 on two occasions. I wonder if earlier references may be more appropriate here (at least in addition to Ref.32). For example, in relation to non-universal contributions due to the Euler characteristic, PRL 97, 050404 (2006); and for entanglement signatures of gapped 3D topological phases, Ref.33

We have added citation of the suggested references on both occasions.

Submission & Refereeing History

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Resubmission 1803.10426v3 on 10 January 2019

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