Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions

Abstract

The ruby lattice is a four-valent lattice interpolating between honeycomb and triangular lattices. In this work we investigate the topological spin-liquid phases of a spin Hamiltonian with Kitaev interactions on the ruby lattice using exact diagonalization and perturbative methods. The latter interactions combined with the structure of the lattice yield a model with ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ gauge symmetry. We mapped out the phase digram of the model and found gapped and gapless spin-liquid phases. While the low energy sector of the gapped phase corresponds to the well-known topological color code model on a honeycomb lattice, the low-energy sector of the gapless phases is described by an effective spin model with three-body interactions on a triangular lattice. A gap is opened in the spectrum in a small magnetic field. We argue that the latter phases could be possibly described by exotic excitations, whose their spectrum is richer than the Ising phase of the Kitaev model.

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Cited by in corpus (5)

• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Topological magnons in Kitaev magnets with finite Dzyaloshinskii-Moriya interaction at high field
• Thermal Hall conductivity with sign change in the Heisenberg-Kitaev kagome magnet
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice