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 SU(2). Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with 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 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 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 U(1) x U(1).