SciPost Submission Page
On symmetry-resolved generalized entropies
by Fei Yan, Sara Murciano, Pasquale Calabrese, Robert Konik
Submission summary
| Authors (as registered SciPost users): | Fei Yan |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2412.14165v1 (pdf) |
| Date submitted: | Jan. 17, 2025, 8:51 p.m. |
| Submitted by: | Yan, Fei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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Abstract
Symmetry-resolved entanglement, capturing the refined structure of quantum entanglement in systems with global symmetries, has attracted a lot of attention recently. In this manuscript, introducing the notion of symmetry-resolved generalized entropies, we aim to develop a computational framework suitable for the study of excited state symmetry-resolved entanglement as well as the dynamical evolution of symmetry-resolved entanglement in symmetry-preserving out-of-equilibrium settings. We illustrate our framework using the example of (1+1)-d free massless compact boson theory, and benchmark our results using lattice computation in the XX chain. As a byproduct, our computational framework also provides access to the probability distribution of the symmetry charge contained within a subsystem and the corresponding full counting statistics.
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
Current status:
Reports on this Submission
Strengths
1- Well-written paper 2- Clear new analytical results
Weaknesses
1- Natural extension of previous work by some of the same authors 2- The relevance to time evolution is not really explored
Report
In this paper, the authors study symmetry-resolved generalized entropies which are relevant to the study of out of equilibrium entanglement in symmetry-preserving setups, or excited states. They perform various exact calculations based on charged moments and replicas on the example of a free compact boson conformal field theory. These results are then checked against lattice fermion computations in the XX chain, with very good agreement.
Overall the manuscript is clearly written, and it contains new results which will be useful to other researcher interested in symmetry resolution in the context of quantum entanglement, or even full counting statistics. For these reasons I recommend publication.
I have two comments:
1) I fail to see the point in the last paragraph in section 1.2. First I would argue that the truncated conformal space approach is already numerical, and the claim that it is 'the only available' method is not really justified in the present manuscript.
2) In appendix C, I find it strange that the authors use Majorana modes instead of complex lattice fermions, since the Hamiltonian is particle-conserving, and the mapping to the bosonic conformal field theory is easier as stated in equation (141). Presumably also, the square-roots would be an artifact of using Majorana modes instead of complex fermions.
Requested changes
I found a typo in page 3: 'an non-abelian' should read 'a non-abelian'.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report
Following the standard approach, the authors first define generalized charged moments and then compute them in the (1+1)-dimensional free massless compact boson theory, a model relevant to various physical systems, such as Luttinger liquids. Explicit analytical expressions are provided for the cases n=1 and n=2, cross-checked against known results, and validated through numerical calculations on the XX spin chain. As an application, the authors compute the generalized subsystem charge distribution, which can be used to study the time evolution of full counting statistics. Finally, they derive the symmetry-resolved generalized second Rényi entropy.
Despite being a straighforward extension of previous work, the results contribute to the advancement of this research area, paving the way for the study of symmetry-resolved entanglement in excited states and symmetry-preserving dynamics. The manuscript is well-written, with clear presentation and detailed computations. For these reasons, I support its publication in SciPost.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)