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Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
by Pengfei Zhang, Chunxiao Liu, Xiao Chen
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Chunxiao Liu · Pengfei Zhang |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2003.09766v2 (pdf) |
| Date accepted: | 2020-06-23 |
| Date submitted: | 2020-03-26 01:00 |
| Submitted by: | Zhang, Pengfei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The Sachdev-Ye-Kitaev model is an $N$-modes fermionic model with infinite range random interactions. In this work, we study the thermal R\'enyi entropy for a subsystem of the SYK model using the path-integral formalism in the large-$N$ limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size $M\leq N/2$. We also consider generalizations of the SYK model with quadratic random hopping term or $U(1)$ charge conservation.
Published as SciPost Phys. 8, 094 (2020)
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2020-5-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2003.09766v2, delivered 2020-05-05, doi: 10.21468/SciPost.Report.1662
Report
This is a solid and technically valid study of the second Renyi entropy of subsystems in the SYK model and its variations. Although the results are as expected and do not present any significant or original insight, I recommend the paper for publishing.
Report #1 by Anonymous (Referee 2) on 2020-4-18 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2003.09766v2, delivered 2020-04-18, doi: 10.21468/SciPost.Report.1626
Strengths
1. Results of wide interest in high energy and condensed matter
2. Comprehensive analysis with numerical and analytic cross-checks
3. Clearly written
Report
This is a comprehensive study of the 2nd Renyi entropy for a subsystem of the SYK model at finite temperature. The authors analyze the SYK model and two of its generalizations: SYK with random hopping, and complex SYK. They derive a large-N saddlepoint formula for the second Renyi entropy by standard methods applied to two replica copies of the SYK model. The saddlepoint equations are solved analytically for small and large subsystems, and numerically in general. The results are compared to the thermal entropy, giving a nontrivial cross-check.
The paper is very clearly written. There is little discussion of physical applications, but it is a solid technical contribution to a subject of growing importance in condensed matter and high energy. I certainly recommend it for publication.