Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

TL;DR

This paper investigates an exactly solvable Gamma matrix generalization of the Kitaev model on the ruby lattice, revealing a complex phase diagram with gapless and gapped phases, and explores perturbations leading to various magnetic orders.

Contribution

It introduces a new exactly solvable model on the ruby lattice and analyzes its phase diagram, including effects of perturbations via mean-field theory.

Findings

Rich phase diagram with gapless and gapped phases

Gapped phases with various Chern numbers

Perturbations lead to trivial and ordered phases

Abstract

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.