Emergent phases in the Yao-Lee model via coupling to topological spin textures

Electrons in metals experience an effective vector potential when coupled to spin textures with non-zero scalar spin chirality, such as skyrmions. This coupling can generate a substantial field, leading to pronounced observable phenomena, including the topological Hall effect. Motivated by this, we consider a bilayer model in which the Majorana fermions in the Yao-Lee model on one layer interact with topological spin textures on the second layer via a spin-spin interaction. Unlike the Kitaev model, the Yao-Lee model remains exactly solvable, allowing us to perform Monte Carlo simulations to determine its ground state. Our analysis indicates that skyrmion crystals can give rise to a variety of vison crystals that are periodic arrangements of the $\mathbb{Z}_2$ fluxes with unusual patterns such as a kagome pattern. In addition, Majorana fermions acquire a substantial Berry phase from skyrmion crystals, resulting in phases with finite Chern numbers up to $\nu =5$. In the case of a single skyrmion defect in the magnetic layer, a corresponding defect in the vison configuration can be realized. These defects support localized states when the spin liquid is gapped. Similar to skyrmion crystals, spiral spin textures also give rise to a diverse range of flux crystals. However, in this case, most of these phases are gapless, with only a few being trivially-gapped. Our results highlight the rich physics emerging from the interplay between topological spin textures and fractionalized quasiparticles in quantum spin liquids.