Polarization-dependent chiral transport and chiral solitons in spin Kitaev models

Recent advances in synthetic quantum matter allow researchers to design quantum models inaccessible in traditional materials. Here, we propose protocols to engineer a new class of quantum spin models, which we call spin Kitaev models. The building blocks are basic spin-exchange interactions combined with locally selective Floquet pulses, a capability recently demonstrated in a range of experimental platforms. The resulting flip-flip and flop-flop terms lead to intriguing quantum transport dynamics beyond conventional spin models. For instance, in the absence of a magnetic field, spin excitations polarized along the $x$ and $y$ axes propagate chirally in opposite directions, producing polarization-dependent spin transport. In the large-spin limit, the spin Kitaev model maps to a nonlinear Hatano-Nelson model, where the interplay of nonlinearity and the underlying curvature yields polarization-dependent chiral solitons. A magnetic field binds two oppositely polarized chiral solitons into a chiral solitonic molecule, whose travel direction depends on its orientation. Our results, directly accessible in current experiments, open new opportunities for simulating transport in curved spaces and for applications in spintronics, information processing, and quantum sensing.