Hyperbolic Spin Liquids

• URL: http://arxiv.org/abs/2407.09601v1
• Date: Fri, 12 Jul 2024 18:00:01 GMT
• Title: Hyperbolic Spin Liquids
• Authors: Patrick M. Lenggenhager, Santanu Dey, Tomáš Bzdušek, Joseph Maciejko,
• Abstract summary: We extend Kitaev's spin 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 $mathbbZ$ spin liquid with Abelian anyons, a gapped chiral spin liquid with non-Abelian anyons and chiral edge states, and a compressible spin liquid with low-energy density of states dominated by non-Abelian Bloch states of Majorana fermions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 compressible spin liquid with low-energy density of states dominated by non-Abelian Bloch states of Majorana fermions.

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