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Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

by Sara Murciano, Giuseppe Di Giulio, Pasquale Calabrese

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Submission summary

Authors (as registered SciPost users): Giuseppe Di Giulio · Sara Murciano
Submission information
Preprint Link:  (pdf)
Date submitted: 2020-01-09 01:00
Submitted by: Murciano, Sara
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.

Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission 1911.09588v3 on 4 March 2020

Reports on this Submission

Anonymous Report 2 on 2020-2-20 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1911.09588v2, delivered 2020-02-20, doi: 10.21468/SciPost.Report.1523


-Pedagogical introduction
-Detailed calculations
-Timely results


In quantum systems with symmetry, the entanglement entropy of a subsystem can be decomposed into contributions coming from different symmetry charge sectors. This leads naturally to the definition of the symmetry-resolved entanglement entropy, which has been the topic of a handful of recent studies.

In this manuscript, the authors compute analytically, using the corner transfer matrix approach, the symmetry-resolved entanglement entropy for two specific integrable models: the complex harmonic chain and the XXZ chain. Some analytic results are supported by numerical calculations. Perhaps most interestingly, the second example was found to satisfy an equipartition of symmetry-resolved entanglement: the entanglement entropy is distributed exactly evenly among the charge sectors. This need not be true generally, and so therefore raises the important question of what is necessary for the equipartition to be satisfied exactly. These results will be a useful reference point for future studies of symmetry-resolved entanglement entropy.

The paper is well written and pedagogical. I support publication of this paper in SciPost as is.

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

Anonymous Report 1 on 2020-2-9 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1911.09588v2, delivered 2020-02-09, doi: 10.21468/SciPost.Report.1485


The paper is well written with all the technical derivations beautifully presented. The physical result of equipartition or lack of it in the different symmetry sectors is very interesting.


Motivation for studying symmetry resolved entanglement is absent.


The paper can be published after the recommended changes are made.

Requested changes

Some more motivation for studying symmetry resolved entanglement is needed. The current manuscript has the following comment in the introduction "it became clear that it is also important to understand the relation between entanglement and symmetries.....", followed by citation
to some papers. I would recommend some more discussion here to strengthen the motivation.

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

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