SciPost Submission Page
Integrable models on Rydberg atom chains
by Luke Corcoran, Marius de Leeuw, Balázs Pozsgay
Submission summary
| Authors (as registered SciPost users): | Luke Corcoran · Balázs Pozsgay |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.15848v2 (pdf) |
| Date submitted: | 2024-08-28 15:19 |
| Submitted by: | Corcoran, Luke |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
We initiate a systematic study of integrable models for spin chains with constrained Hilbert spaces; we focus on spin-1/2 chains with the Rydberg constraint. We extend earlier results for medium-range spin chains to the constrained Hilbert space, and formulate an integrability condition. This enables us to construct new integrable models with fixed interaction ranges. We classify all time- and space-reflection symmetric integrable Rydberg-constrained Hamiltonians of range 3 and 4. At range 3, we find a single family of integrable Hamiltonians: the so-called RSOS quantum chains, which are related to the well-known RSOS models of Andrews, Baxter, and Forrester. At range 4 we find two families of models, the first of which is the constrained XXZ model. We also find a new family of models depending on a single coupling $z$. We provide evidence of two critical points related to the golden ratio $\phi$, at $z=\phi^{-1/2}$ and $z=\phi^{3/2}$. We also perform a partial classification of integrable Hamiltonians for range 5.
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
1. Paper addresses a timely and interesting question at the intersection of two fields: integrability and constrained models.
2. Paper presents details in the clear form, and results can be readily used by the community.
Weaknesses
1. Paper is written in a somewhat overly technical way. While it is impossible to avoid technical language in a field of integrability, I still believe that some things can be explained more intuitively/deciphered.
2. In some places it would be nice to expand the paper with the examples.
Report
The paper addresses a timely and interesting question at the intersection of two fields: integrability and constrained models. The main results of the paper are new families of integrable constrained models, beyond those known in the literature. I find these results highly interesting and non-trivial, as integrable models often allow unique insights into the physics due to their analytical solvability.
I am not an expert in integrability, but some of the checks confirm self-consistency of results. In particular, the dependence of Eq. (6) on parameter z is consistent with spectral reflection property (existence of operator C = prod sigma^z that changes sign of some terms in the Hamiltonian, thus mapping z->-z effectively).
While I am happy to recommend the publication without any changes, I invite authors to address some of my comments to improve the readability and presentation of the paper.
Requested changes
General comments:
1. It would be nice to comment if models found by authors have many-body chiral symmetry, i.e. if there exists points where some operator C satisfies {C,H} =CH+HC=0.
2. When deriving families of models, it would be interesting to see the flavor of algebraic equations derived for free parameters.
3. Would be nice to have some discussion of connection between list of bullet points on page 8 and 16 (if it exists).
4. Section 6 has only one subsection. Please restructure.
5. Another interesting speculative point for discussion would be the possibility of disordered (with correlated disorder) constrained integrable models. Would the author's method be capable of finding such models?
Most of changes are minor and would improve readability:
1. The very first sentence in the paper would benefit from rephrasing: it is too vague.
2. Same first paragraph term "algebraic origin" is not quite clear
3. Some terms would be good to unpack for a non-expert audience, for instance algebraic Bethe ansatz, Reshetikhin conditions, RLL relation,... by just explaining their essence/flavor. This will improve the readability for non-experts in integrability.
3. References on Page 3 [32,...] are grouped into strange groups. Join them or explain.
4. Footnote 1 should be after the dot.
5. Explicitly mark special points that are studied in Fig 11 on the x-axis of Fig. 10
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)