SciPost Submission Page

Universal entanglement signatures of foliated fracton phases

by Wilbur Shirley, Kevin Slagle, Xie Chen

This is not the current version.

Submission summary

As Contributors: Wilbur Shirley · Kevin Slagle
Arxiv Link:
Date submitted: 2018-05-27
Submitted by: Shirley, Wilbur
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Condensed Matter Physics - Theory


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.

Current status:
Has been resubmitted

Ontology / Topics

See full Ontology or Topics database.


Submission & Refereeing History

Resubmission 1803.10426v3 on 10 January 2019
Submission 1803.10426v1 on 27 May 2018

Reports on this Submission

Anonymous Report 2 on 2018-6-23 Invited Report


1) this paper addresses the open question of understanding entanglement in foliated fracton phases

2) the authors study the different contribution to the entanglement entropy and propose schemes to distil a universal contribution, using multipartite entanglement measures

3) they show that the proposed universal signatures are constant throughout foliated fracton phases, by explicit calculation in a handful of model Hamiltonians


1) it is not clear what to make of these universal signatures, why are they important, and whether they will have an impact on the related area of research. Further work is perhaps needed to better understand their significance, and possibly their relation to the structure of the excitations


the paper is well structured and well written, accessible to a reader with some background on topological lattice models, entanglement entropy, and fracton phases. The results are valid, to the best of my understanding, and deserve publication in SciPost.

Requested changes

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)

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

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

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

  • validity: good
  • significance: ok
  • originality: ok
  • clarity: good
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2018-6-21 Invited Report


1. Clear calculations
2. Well written


1. Narrow focus
2. Interest to non-experts unclear.


This is a solid and well written paper on an interesting topic. I recommend publication as is.

Requested changes


  • validity: high
  • significance: ok
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Login to report or comment