Kitaev model in regular hyperbolic tilings

• URL: http://arxiv.org/abs/2506.17981v1
• Date: Sun, 22 Jun 2025 10:44:53 GMT
• Title: Kitaev model in regular hyperbolic tilings
• Authors: Julien Vidal, Rémy Mosseri,
• Abstract summary: We study the Kitaev model on regular hyperbolic trivalent tilings.<n>We compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the Kitaev model on regular hyperbolic trivalent tilings. Depending on the length $p$ of the elementary polygons, we examine two distinct tri-colorings of the tiling. Using a recent conjecture on the ground-state flux sector, we compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians in the isolated-dimer limit which are valid for all values of $p$. Our results interpolates between the Euclidean honeycomb lattice and the trivalent Bethe lattice ($p=\infty$) for which we derive the exact solution of the phase boundaries.

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