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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: | 2025-01-17 20:51 |
| 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
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In this manuscript, the authors introduce the concept of symmetry-resolved generalized entropies and apply it to systems with a global U(1) symmetry. The aim is to provide a framework for studying symmetry-resolved entanglement in excited states beyond the lowest-energy ones, as well as its evolution in symmetry-preserving out-of-equilibrium settings. The study of symmetry resolution in entanglement measures has gained significant attention in recent years, offering a more refined understanding of the structure of entanglement by decomposing contributions from different symmetry sectors.
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.
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