Skyrmions of Frustrated Quantum Dimer Systems

Magnetic skyrmions are topologically protected solitons observed in various classes of real magnets. In two-dimensional systems, where the target space of local magnetization values is the two-sphere S², skyrmion textures are classified by the homotopy classes of two-loops S² in S²: Π₂ (S²)≅Ζ. Here, we demonstrate that more general topological skyrmion textures emerge in the classical limit of quantum dimer systems, where the phase space of the relevant classical theory is CP^N-1 (with N=4 for the case of interest), because the relevant second homotopy group, Π₂ (CP^N-1)≅Ζ for N ≥ 2, remains unchanged. Building on the framework established by Zhang et al. (2023), we consider a classical limit based on SU(4) coherent states, which preserve intra-dimer entanglement. We show that the zero-temperature phase diagram of frustrated spin-dimer systems on a bilayer triangular lattice with weak inter-dimer coupling includes two magnetic-field-induced CP³ skyrmion crystal phases.