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Finite-size corrections in critical symmetry-resolved entanglement
by Benoit Estienne, Yacine Ikhlef, Alexi Morin-Duchesne
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|Benoit Estienne · Yacine Ikhlef · Alexi Morin-Duchesne
In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.
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- Cite as: Anonymous, Report on arXiv:2010.10515v2, delivered 2021-01-01, doi: 10.21468/SciPost.Report.2349
1- Very well-written paper, easy to follow
2- Nice CFT calculations, complemented by thorough numerical checks
In this paper, the authors study the finite-size corrections to symmetry-resolved entanglement in 1+1d CFTs. They find that corrections to entropy equipartition depend crucially on whether the symmetry group is discrete or continuous: for discrete symmetries, the corrections are algebraic, while in the case of a U(1) symmetry, the corrections decay logarithmically with system size. They also identify the prefactors of these corrections with some overlaps that can be computed numerically or analytically in some cases.
This work contains interesting results in a timely area of research. The manuscript is very well written, and easy to follow. I do not have any particular suggestion to improve the presentation, and I strongly recommend publication in SciPost as is.
- Cite as: Anonymous, Report on arXiv:2010.10515v2, delivered 2020-12-18, doi: 10.21468/SciPost.Report.2310
1-very well explained and written
2- extensive and careful study using state-of-the-art techniques
3- excellent verification of the results
In this paper the authors study the finite-size corrections to the symmetry resolved entanglement entropies in systems described by conformal field theories. In the
scaling limit of large systems the entanglement entropies exhibit equipartition, i.e, they become independent on the symmetry sector. The authors show that the subleading finite-size corrections depend on the nature of the symmetry. For continuous symmetry they find that the corrections are logarithmic, whereas for discrete symmetry they are algebraic. The authors carefully check their findings numerically.
This is a very interesting paper which provides top-quality results on a timely topic. The paper provides an in-depth understanding of the origin of the finite-size corrections to the symmetry-resolved entanglement entropies. Moreover, to my knowledge the authors are the first to highlight the difference between continuous and discrete symmetries.
I have only one important observation:
1) The fact that the symmetry-resolved entanglement entropies exhibit
logarithmic corrections remains true also in the presence of disorder. This
has been studied recently in
Phys. Rev. B 102, 014455 (2020)
the authors could mention this paper.
1-some of the qualitative behaviors described are not new.