Hyperbolic Spin Liquids

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 ${\mathbb{Z}}_2$ 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.

6 pages (7 figures) + references + 32 pages of Supplemental Material (18 figures + 1 table); (v2) updated with accepted version

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Cited by in corpus (5)

• Bose-Einstein condensation in exotic lattice geometries
• Quantum geometric tensors from sub-bundle geometry
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Classical spin liquids from frustrated Ising models in hyperbolic space