Skyrmions of Frustrated Quantum Dimer Systems

Abstract

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 $S^2$, skyrmion textures are classified by the homotopy classes of two-loops $S^2$ in $S^2$: ${\Pi }_2(S^2)\cong Z$. 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 ${\mathbb{CP}}^{N-1}$ (with $N=4$ for the case of interest), because the relevant second homotopy group, ${\Pi }_2({\mathbb{CP}}^{N-1})\cong Z$ for $N\ge 2$, 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 ${\mathbb{CP}}^3$ skyrmion crystal phases.

17 pages, 12 figures