Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice
Abstract
We study the spin-1/2 Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice with a symmetry-preserving tri-coloring of the Kitaev exchanges. We focus on two cases: (i) the pure Kitaev model with anisotropic exchanges and (ii) the Kitaev-Heisenberg model with isotropic Kitaev exchange. In the absence of Heisenberg interactions, we use the standard mapping of the Kitaev model onto a quadratic Majorana-fermion problem in a ℤ2 gauge field. We find a gapped energy spectrum throughout the positive-coupling phase diagram, except at a single point where the twofold-degenerate energy bands form a Dirac cone. This unique gapped region corresponds to a toric code phase. However, depending on the couplings, vortex excitations on square, hexagonal, and dodecagonal plaquettes realize three distinct relative assignments to the e and m anyons. We determine these relative assignments from the physical fermion parity of the vortex sectors and locate their boundaries by tracking zero crossings of vortex-bound Majorana levels. For the isotropic Kitaev-Heisenberg model, we combine graph-based projected entangled-pair-state calculations, exact diagonalizations, and linear spin-wave theory to study the entire phase diagram. Apart from the toric code topological phases that are robust around the Kitaev limits, we obtain four collinear magnetically ordered phases that can be characterized by their local and relative orderings of hexagonal plaquettes. We also identify a special point at which the ground state is a product state.
Related
- Kitaev, semi-Dirac, and spinon quantum spin Hall liquids on the square-hexagon-dodecagon lattice: A parent projective symmetry group classification
- Establishing Néel order in the square-lattice antiferromagnetic Heisenberg model: a bootstrap proof
- Weak ferromagnetism in the square-lattice Heisenberg J1-J2-J2′ model with easy-axis single-ion anisotropy
- Schwinger boson perturbation theory for spin-S Kitaev-Heisenberg magnets: phase diagram and dynamical response near Kitaev spin liquids
- Gottesman-Kitaev-Preskill codes: A lattice perspective
BibTeX
@misc{barari2026kitaevheisenberg,
title = {{Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice}},
author = {Saeed Barari and Yasir Iqbal and Ganapathy Baskaran and Saeed S. Jahromi and Chunxiao Liu and Julien Vidal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33454},
eprint = {2609.33454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33454},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice
AU - Saeed Barari
AU - Yasir Iqbal
AU - Ganapathy Baskaran
AU - Saeed S. Jahromi
AU - Chunxiao Liu
AU - Julien Vidal
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33454
UR - https://arxiv.org/abs/2609.33454
AB - We study the spin-1/2 Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice with a symmetry-preserving tri-coloring of the Kitaev exchanges. We focus on two cases: (i) the pure Kitaev model with anisotropic exchanges and (ii) the Kitaev-Heisenberg model with isotropic Kitaev exchange. In the absence of Heisenberg interactions, we use the standard mapping of the Kitaev model onto a quadratic Majorana-fermion problem in a ℤ_2 gauge field. We find a gapped energy spectrum throughout the positive-coupling phase diagram, except at a single point where the twofold-degenerate energy bands form a Dirac cone. This unique gapped region corresponds to a toric code phase. However, depending on the couplings, vortex excitations on square, hexagonal, and dodecagonal plaquettes realize three distinct relative assignments to the e and m anyons. We determine these relative assignments from the physical fermion parity of the vortex sectors and locate their boundaries by tracking zero crossings of vortex-bound Majorana levels. For the isotropic Kitaev-Heisenberg model, we combine graph-based projected entangled-pair-state calculations, exact diagonalizations, and linear spin-wave theory to study the entire phase diagram. Apart from the toric code topological phases that are robust around the Kitaev limits, we obtain four collinear magnetically ordered phases that can be characterized by their local and relative orderings of hexagonal plaquettes. We also identify a special point at which the ground state is a product state.
ER -