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arXiv · 2407.09601

Hyperbolic Spin Liquids

Patrick M. Lenggenhager·Santanu Dey·Tomáš Bzdušek·Joseph Maciejko
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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.

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Patrick M. Lenggenhager, Santanu Dey, Tomáš Bzdušek, Joseph Maciejko. 2024-07-12. Hyperbolic Spin Liquids. https://doi.org/10.1103/s25y-s4fj

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