@article{Dey:2024,
    title               = {Hyperbolic Spin Liquids}, 
    author              = {Patrick M. Lenggenhager, Santanu Dey, Tomáš Bzdušek, Joseph Maciejko},
    journal             = {arXiv preprint},
    year                = {2024},
    doi                 = {10.48550/arXiv.2407.09601},
    url                 = {https://arxiv.org/abs/2407.09601}
    eprint              = {2407.09601},
    eprintType          = {arXiv},
    archivePrefix       = {arXiv}
}

P. M. Lenggenhager, S. Dey, T. Bzdušek, and J. Maciejko

arXiv:2407.09601 (2024) – Published 12 Jul 2024

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 compressible spin liquid with low-energy density of states dominated by non-Abelian Bloch states of Majorana fermions.