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

Abstract

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 ν and an associated chiral central charge c_{-} = ν/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.

arXiv comment9 pages, 6 figures

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• Microscopic Roadmap to a Yao-Lee Spin-Orbital Liquid
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Magnetic order through Kondo coupling to quantum spin liquids
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking