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Ergodic Archimedean dimers
by Henrik Schou Røising, Zhao Zhang
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Zhao Zhang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202306_00032v1 (pdf) |
| Date accepted: | 2023-07-18 |
| Date submitted: | 2023-06-23 16:49 |
| Submitted by: | Zhang, Zhao |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.
Author comments upon resubmission
We thank you kindly for the consideration of our manuscript, and we thank the referees for their helpful and accurate evaluations of our work. We accept the recommendation of the editor and the referees and hereby resubmit our manuscript to be considered for SciPost Physics Core. All referee comments have been taken into account in the resubmitted manuscript, with a list of changes and a revised manuscript with changes marked in red attached.
Kind regards,
Henrik S. Røising and Zhao Zhang
List of changes
1) All referee comments have been addressed with rectified text marked in red in the attached manuscript.
2) Name "star" added to the (3, 12^2) lattice in Fig. 2.
3) In Eq. (2) and (3) the summation over l (rotations) has been updated to l = 0,1,2 (instead of l = 1,2,3) and correspondingly the l's in the rest of this section (Fig. 7, Eq. (4), (5), and the surrounding text) have been rectified to correct for a notational inconsistency in the previous version.
4) Three sentences on generalized domino tilings have been added at the end of the fourth paragraph in the Conclusions.
5) References 34, 35, 48, 49, and 56 have been added.
Published as SciPost Phys. Core 6, 054 (2023)