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

TL;DR

This paper investigates topological solitons in an $SU(3)$ symmetric cold atom model on a triangular lattice, revealing stable and unstable soliton configurations and proposing new quantum phases with emergent interactions.

Contribution

It introduces a novel family of topological solitons with integer charges in an $SU(3)$ symmetric system and analyzes their stability and interactions using homotopy, field theory, and variational methods.

Findings

Stable solitons with charge (Q, -Q, 0) identified

Unstable general charge solitons decay into pairs

Potential realization of interacting solitons and new quantum spin liquids

Abstract

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 new family of solitonic wave functions characterised by integer charge ${\bf Q} = (Q_A, Q_B, Q_C)$, 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, while solitons with charge ${\bf Q} = (Q, -Q, 0)$ are stable, wave functions with more general charge spontaneously decay into pairs of solitons with emergent interactions. This result suggests that it could be possible to realise a new class of interacting soliton, with no classical analogue, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge--group U(1)$\times$U(1).