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Hyperbolic Spin Liquids

Patrick M. Lenggenhager1,*, Santanu Dey2,3, Tomáš Bzdušek4, and Joseph Maciejko2,5,†

  • *Contact author: plengg@pks.mpg.de
  • †Contact author: maciejko@ualberta.ca
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Phys. Rev. Lett. 135, 076604 – Published 15 August, 2025

DOI: https://doi.org/10.1103/s25y-s4fj

Abstract

Hyperbolic lattices present a unique opportunity to venture beyond the conventional paradigm of crystalline many-body physics and explore correlated phenomena in negatively curved space. As a theoretical benchmark for such investigations, we extend Kitaev’s spin-1/2 honeycomb model to hyperbolic lattices and exploit their non-Euclidean space-group symmetries to solve the model exactly. We elucidate the ground-state phase diagram on the {8,3} lattice and find a gapped Z2 spin liquid with Abelian anyons, a gapped chiral spin liquid with non-Abelian anyons and chiral edge states, and a Majorana metal whose finite low-energy density of states is dominated by non-Abelian Bloch states.

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Phys. Rev. Lett. 135, 076604– Published 15 August, 2025
  • Received 19 July 2024
  • Revised 19 December 2024
  • Accepted 7 July 2025
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