Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $\text{SU}\left(2\right)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $\text{SU}\left(3\right)$ symmetry. Using a combination of homotopy analysis and analytic field theory we identify a family of solitonic wave functions characterized by integer charge $\mathbf{Q}=(Q_A,Q_B,Q_C)$, with $Q_A+Q_B+Q_C=0$. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that solitons with charge $\mathbf{Q}=(1,1,-2)$ spontaneously decay into a pair of solitons with elementary topological charge, and emergent interactions. This result suggests that it could be possible to realize a class of interacting soliton, with no classical analog, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge group $\text{U}\left(1\right)\times \text{U}\left(1\right)$.

• Received 30 October 2015

DOI:https://doi.org/10.1103/PhysRevA.93.021606