Skyrmions of Frustrated Quantum Dimer Systems

TL;DR

This paper reveals that classical limits of quantum dimer systems can host topologically protected skyrmion textures in phase spaces modeled by complex projective spaces, expanding the understanding of skyrmions beyond traditional magnetization contexts.

Contribution

It demonstrates the emergence of $ ext{CP}^{N-1}$ skyrmion textures in quantum dimer systems' classical limit, specifically identifying two skyrmion crystal phases in a frustrated bilayer triangular lattice.

Findings

Identification of $ ext{CP}^{3}$ skyrmion crystal phases in the phase diagram.

Extension of skyrmion classification to complex projective phase spaces.

Preservation of topological properties in the classical limit of quantum dimer models.

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 $N\geq 2$, 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.