Integrable models on Rydberg atom chains

TL;DR

This paper systematically studies integrable spin chain models with Rydberg constraints, extending previous results, classifying models of certain ranges, and identifying new integrable families and critical points.

Contribution

It introduces a new integrability condition for constrained spin chains, classifies all symmetric integrable Hamiltonians of ranges 3 and 4, and discovers new integrable models and critical points.

Findings

Classified all symmetric integrable Hamiltonians of range 3 and 4.

Identified a new family of models depending on a coupling z.

Found critical points related to the golden ratio at specific couplings.

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.