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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 | |
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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 | |
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Academic field: | Physics |
Specialties: |
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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.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block