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Resonant Valance Bond Ground States on Corner-sharing Lattices
by Zhao Zhang, Cecilie Glittum
Submission summary
| Authors (as registered SciPost users): | Cecilie Glittum · Zhao Zhang |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2507.10471v2 (pdf) |
| Date submitted: | Nov. 7, 2025, 5:11 p.m. |
| Submitted by: | Cecilie Glittum |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The Hubbard model in the $U\to\infty$ limit has recently been shown to have resonant valence bond (RVB) ground states on the corner-sharing sawtooth and pyrochlore lattices in the dilute doping limit of a single vacancy. The two results were obtained by different approaches which do not apply to one another. We make the first step towards unifying them by studying the quasi-1D lattice of a pyrochlore stripe, where all corners are not shared between two tetrahedra, and the valence bond configurations are not fixed by the location of the vacancy. The energy level ordering of irreducible representations of each tetrahedron shows that a chain of them has exponentially degenerate partial RVB or dimer-monomer ground states where each tetrahedron hosts one spin-$1/2$ monomer and one spin-$0$ dimer. The exact ground states in the infinitely long chain limit are analytically solved by introducing basis transformations between local Hilbert spaces of neighboring tetrahedra, and its energy agrees with the extrapolation of numerical exact diagonalization results of finite sized systems.
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
Report #1 by Anonymous (Referee 1) on 2026-1-7 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
ChatGPT 5.2 was used (7. January) to check gramma and spelling of my comment, since I am no native speaker.
Report
Overall, the paper is highly relevant, as it may open a route to understanding the model studied in Ref. [10] from a different perspective and could guide investigations of other one-dimensional models with similar features. The manuscript is well structured and clearly written; nevertheless, I have a few minor comments and suggested changes, as detailed below.
Requested changes
1- On page 3, in footnote 2, the last sentence appears to be incomplete. 2- I do not see how the normalization factors $\dfrac{1}{\sqrt{6}}$ in Fig. 5 are obtained. 3-I would not object to renaming the “flux inequality” as the “diamagnetic inequality,” since this is the terminology most commonly used in the literature, including in the cited references. 4-The manuscript states that inequality (20) is “obviously” true because inequality (21) holds. However, it is not clear to me (i) why inequality (21) holds and (ii) how (20), in its squared form, follows from it. A few sentences clarifying these steps would be useful.
Recommendation
Publish (meets expectations and criteria for this Journal)