Kitaev model in regular hyperbolic tilings

TL;DR

This paper investigates the Kitaev model on hyperbolic tilings, deriving phase diagrams and effective Hamiltonians that interpolate between known Euclidean and Bethe lattice cases, expanding understanding of quantum spin liquids in hyperbolic geometries.

Contribution

It provides analytical and numerical analysis of the Kitaev model on hyperbolic tilings, including phase diagrams and effective Hamiltonians for all polygon lengths p.

Findings

Derived phase boundaries for hyperbolic Kitaev models.

Provided analytical expressions for effective Hamiltonians.

Connected hyperbolic models to Euclidean and Bethe lattice limits.

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 interpolate between the Euclidean honeycomb lattice and the trivalent Bethe lattice ($p=\infty$) for which we derive the exact solution of the phase boundaries.