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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Patrick M. Lenggenhager
Santanu Dey
Tomáš Bzdušek
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Lenggenhager et al. (Fri,) studied this question.
synapsesocial.com/papers/6980fc91c1c9540dea80e52d — DOI: https://doi.org/10.5167/uzh-283330