Inherent altermagnetism in minimal tight-binding models of regular hyperbolic lattices
Abstract
Altermagnets are a novel class of magnetic systems characterized by their momentum-dependent spin splitting without net magnetization. In this work, we extend established Euclidean tight-binding models of altermagnets to regular hyperbolic lattices in two spatial dimensions defined on a discretized Poincaré disk. Using hyperbolic crystallography and Abelian hyperbolic band theory, we show that the inclusion of next-nearest neighbor hopping is sufficient to induce spin splitting in minimal tight-binding models of bipartite hyperbolic lattices. While certain families and special cases of hyperbolic lattices remain antiferromagnetic, we identify an entire family and a special case that generically permit spin splitting in this framework. Hence, altermagnetism is inherent to certain hyperbolic lattices. Since Abelian hyperbolic band theory yields a momentum space that is at least four-dimensional, we classify the leading spin-splitting harmonics using four-dimensional atomic orbitals. As an outlook, we apply non-Abelian hyperbolic band theory to the {10,5} lattice. Although its Abelian spectrum is spin degenerate, two selected higher-genus supercells exhibit spin splitting. This finding suggests, that spin degeneracy does not necessarily persist within all translation representation sectors.
Versions
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BibTeX
@misc{petermann2026inherent,
title = {{Inherent altermagnetism in minimal tight-binding models of regular hyperbolic lattices}},
author = {Eric Petermann and Kristian Mæland and Haye Hinrichsen and Björn Trauzettel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.10602},
eprint = {2605.10602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10602},
}
RIS
TY - UNPB
TI - Inherent altermagnetism in minimal tight-binding models of regular hyperbolic lattices
AU - Eric Petermann
AU - Kristian Mæland
AU - Haye Hinrichsen
AU - Björn Trauzettel
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2605.10602
UR - https://arxiv.org/abs/2605.10602
AB - Altermagnets are a novel class of magnetic systems characterized by their momentum-dependent spin splitting without net magnetization. In this work, we extend established Euclidean tight-binding models of altermagnets to regular hyperbolic lattices in two spatial dimensions defined on a discretized Poincaré disk. Using hyperbolic crystallography and Abelian hyperbolic band theory, we show that the inclusion of next-nearest neighbor hopping is sufficient to induce spin splitting in minimal tight-binding models of bipartite hyperbolic lattices. While certain families and special cases of hyperbolic lattices remain antiferromagnetic, we identify an entire family and a special case that generically permit spin splitting in this framework. Hence, altermagnetism is inherent to certain hyperbolic lattices. Since Abelian hyperbolic band theory yields a momentum space that is at least four-dimensional, we classify the leading spin-splitting harmonics using four-dimensional atomic orbitals. As an outlook, we apply non-Abelian hyperbolic band theory to the {10,5} lattice. Although its Abelian spectrum is spin degenerate, two selected higher-genus supercells exhibit spin splitting. This finding suggests, that spin degeneracy does not necessarily persist within all translation representation sectors.
ER -