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

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 $\mathbf{Q}=(Q_A,Q_B,Q_C)$, 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, while solitons with charge $\mathbf{Q}=(Q,-Q,0)$ 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).

8 pages, 5 figures

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Cited by in corpus (21)

• Topological spin crystals by itinerant frustration
• Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1{)}^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• SU(3) Topology of Magnon-Phonon Hybridization in 2D Antiferromagnets
• Generalization of the Haldane conjecture to SU(3) chains
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields
• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
• Semi-classical simulation of spin-1 magnets
• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• CP${}^2$ Skyrmions and Skyrmion Crystals in Realistic Quantum Magnets
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Self-conjugate representation SU(3) chains
• Gravitational wave analogues in spin nematics and cold atoms
• BPS Sphalerons in the $F_2$ Non-Linear Sigma Model
• Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice
• Orbital moiré and quadrupolar triple-q physics in a triangular lattice
• Influence of topological constraints and topological excitations: Decomposition formulas for calculating homotopy groups of symmetry-broken phases
• Quantum Interactions of Topological Solitons from Electrodynamics