Kitaev model in regular hyperbolic tilings

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.

9 pages, 10 figures, published version

References in corpus (21)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Zoo of quantum-topological phases of matter
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• An exact chiral spin liquid with non-Abelian anyons
• Exactly solvable Kitaev model in three dimensions
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Physical solutions of the Kitaev honeycomb model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Universality of Hofstadter butterflies on hyperbolic lattices
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• The Wavefunction of an Anyon
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Density of states of tight-binding models in the hyperbolic plane
• Anderson localization transition in disordered hyperbolic lattices
• Kitaev Quantum Spin Liquids
• An Exact Chiral Amorphous Spin Liquid
• Kitaev model and dimer coverings on the honeycomb lattice
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid

Cited by in corpus (3)

• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Topological states and flat bands in exactly solvable decorated Cayley trees