Magnetically ordered yet topologically robust phases emerging in concurrent Kitaev spin liquids

TL;DR

This paper explores the phase diagram of the Yao-Lee model with added Kitaev and Heisenberg interactions, revealing coexistence of magnetic order and topologically robust spin liquid phases.

Contribution

It introduces an analysis of the Yao-Lee model with perturbations, showing how magnetic and topological phases coexist and evolve.

Findings

Magnetic order can coexist with a spin liquid orbital sector.

Both sectors form liquid phases when Yao-Lee interactions dominate.

Heisenberg exchange influences the stability of magnetic and topological phases.

Abstract

Spin-orbital generalizations of Kitaev model, such as Yao-Lee model, have attracted recent attention due to their enhanced stability of spin liquid phases against perturbations. Motivated by microscopic calculations for the realization of Yao-Lee model showing additional interactions, we study the phase diagram of the Yao-Lee model with added Kitaev and Heisenberg terms. While the plaquette operator is conserved even in the presence of added perturbations, the model becomes no longer exactly solvable. Using perturbation and Majorana mean-field theory, we find magnetic order can arise in the spin sector while the orbital sector remains a liquid for dominant Kitaev interactions, whereas both sectors form liquid phases when Yao-Lee interactions dominate. Additional Heisenberg exchange can enhance or suppress the magnetic order, revealing a rich coexistence of magnetic and topological phases.