Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions

TL;DR

This paper explores topological spin-liquid phases on the ruby lattice with anisotropic Kitaev interactions, revealing both gapped and gapless phases with potential for exotic excitations and topological quantum computation.

Contribution

It introduces a detailed phase diagram of the Kitaev model on the ruby lattice, identifying new gapped and gapless spin-liquid phases with complex gauge symmetries.

Findings

Identified gapped and gapless spin-liquid phases.

Mapped the phase diagram of the model.

Found potential for exotic excitations in certain phases.

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.