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  • Letter
  • Open Access

Integrable and critical Haagerup spin chains

Luke Corcoran* and Marius de Leeuw†

  • *Contact author: lcorcoran@maths.tcd.ie
  • †Contact author: mdeleeuw@maths.tcd.ie
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Phys. Rev. B 111, L140408 – Published 16 April, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L140408

Abstract

We construct the first integrable models based on the Haagerup fusion category H3. 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 H3 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.

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Outline

Information

Phys. Rev. B 111, L140408– Published 16 April, 2025
  • Received 14 November 2024
  • Revised 21 February 2025
  • Accepted 7 April 2025
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