Vison crystals, chiral and crystalline phases in the Yao-Lee model

We study the phase diagram of the Yao-Lee model with Kitaev-type spin-orbital interactions in the presence of Dzyaloshinskii-Moriya interactions and external magnetic fields. Unlike the Kitaev model, the Yao-Lee model can still be solved exactly under these perturbations due to the enlarged local Hilbert space. Through a variational analysis, we obtain a rich ground state phase diagram that consists of a variety of vison crystals with periodic arrangements of background Z2 flux (i.e. visons). With an out-of-plane magnetic field, these phases have gapped bulk and chiral edge states, characterized by a Chern number {\nu} and an associated chiral central charge c_{-} = {\nu}/2 of edge states. We also find helical Majorana edge states that are protected by magnetic mirror symmetry. Our results spotlight the tunability and the accompanying rich physics in exactly-solvable spin-orbital generalizations of the Kitaev model.