Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice

Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $\text{SU}(2)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $\text{SU}(3)$ 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 $\mathbf{Q}=(1,1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}2)$ 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 $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$.