Year: 2025
Type: article
Abstract: We construct the first integrable models based on the Haagerup fusion category H 3 . We introduce a Haagerup version of the anyonic spin chain and use the boost operator formalism to identify two integrable Hamiltonians of PXP type on this chain. The first of these is an analog of the golden chain; it has a topological symmetry based on H 3 and satisfies the Temperley-Lieb algebra with parameter δ = ( 3 + 13 ) / 2 . We prove its integrability using a Lax formalism, and construct the corresponding solution to the Yang-Baxter equation. We present numerical evidence that this model is gapless with a dynamical critical exponent z ≠ 1 . The second integrable model we find breaks the topological symmetry. We present numerical evidence that this model reduces to a CFT in the large volume limit with central charge c ∼ 3 / 2 .
Authors: Luke Corcoran, Marius de Leeuw
Institution: Trinity College Dublin
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Funders: Royal Society, Science Foundation Ireland
OpenAlex ID: W4409499313