SciPost Submission Page
Highly Entangled 2D Ground States: Tensor Networks and Correlation Functions
by Olai B. Mykland, Zhao Zhang
Submission summary
| Authors (as registered SciPost users): | Zhao Zhang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202503_00047v1 (pdf) |
| Date submitted: | March 25, 2025, 12:16 p.m. |
| Submitted by: | Zhao Zhang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tessellation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.
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
Report
On page 2, the authors mention the entanglement entropy of "free fermionic systems with a Fermi sea in any dimension," citing Ref. [9]. I suggest replacing "Fermi sea" with "Fermi surface": the term "Fermi sea" could also refer to a gapped situation (e.g., a fully occupied band separated by an empty band with a gap) or systems with only Dirac points, where the area law is restored without a logarithmic violation. In addition, the parallel work by M. Wolf, Phys. Rev. Lett. 96, 010404 (2006), published back-to-back with Ref. [9], should also be cited. Both papers independently established the logarithmic violation of the area law for free fermions with a Fermi surface.
Regarding the higher-dimensional generalization related to Ref. [10], the authors currently cite Ref. [11] only. However, an earlier contribution by G. Sierra and collaborators, J. Stat. Mech. (2015) P06002, should also be cited for completeness.
Other than these points, I have no major criticisms. The technical constructions in the main sections appear correct and carefully explained.
In conclusion, I recommend publication in SciPost Physics once the above citation issues are addressed.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
1- Non trivial results 2- novel construction of a 3d exact tensor network describing the ground state of a 2D quantum model 3- The paper supplies clear motivations and background material
Weaknesses
1- Results are of academic interest 2- Require significant effort to fully understand.
Report
The results serve to complete an obvious next step in the field of highly entangled states - that of an explicit tensor network in 3D, and as such are of sufficient quality and interest for publication.
The only thing I would suggest that can improve the paper, but this is optional (I would at least suggest that the authors do that if they give talks on the subject!) is to find a way to illustrate the actual 3D construction in a more intuitive way than just listing the prisms that do the job.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)