SciPost Submission Page
Non-abelian symmetry-resolved entanglement entropy
by Eugenio Bianchi, Pietro Dona, Rishabh Kumar
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Eugenio Bianchi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00030v2 (pdf) |
| Date accepted: | 2024-10-21 |
| Date submitted: | 2024-10-03 19:03 |
| Submitted by: | Bianchi, Eugenio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
List of changes:
- Added remarks;
- Added table;
- Typos fixed;
- References added.
To help identifying the changes we highlighted them in red in the version attached to the referee responses.
Published as SciPost Phys. 17, 127 (2024)
Reports on this Submission
Report
I thank the authors for implementing the requested changes. I think that the further explanations and the comparisons with the existing literature have significantly improved the clarity of the paper and I recommend it for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
Same as in my first report
Weaknesses
The main weakness for me was that the mathematical nature of the work obscured the physical applications. This has been improved considerably in the 2nd version.
Report
The authors have submitted a revised version of their paper which answers my (minor) comments and those of the other referee. We both had rather similar comment in fact and the authors have made a considerable effort to comment on those, in particular to explain more clearly what they compute and how it might apply to specific types of theories. I recommend that the paper is now published.
Requested changes
None.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)