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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:
  • High-Energy Physics - Theory
  • Mathematical Physics
  • Quantum Physics
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:
In refereeing

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