Order-by-Disorder Degeneracy Lifting of Interacting Bosons on the Dice Lattice

Abstract

Motivated by recent experimental progress in the realization of synthetic gauge fields in systems of ultracold atoms, we consider interacting bosons on the dice lattice with half flux per plaquette. All bands of the non-interacting spectrum of this system were previously found to have the remarkable property of being completely dispersionless. We show that degeneracies remain when interactions are treated at the level of mean field theory, and the ground state exhibits vortex lattice configurations already established in the simpler XY model in the same geometry. We argue that including quantum and thermal fluctuations will select a unique vortex lattice up to overall symmetries based on the order-by-disorder mechanism. We verify the stability of the selected state by analyzing the condensate depletion. The latter is shown to exhibit an unusual non-monotonic behavior as a function of the interaction parameters which can be understood as a consequence of the dispersionless nature of the non-interacting spectrum. Finally, we comment on the role of domain walls which have interactions mediated through fluctuations.

9 pages, 5 figures

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• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Bose condensation in flat bands
• Topological orbital ladders
• Orbital order in Mott insulators of spinless p-band fermions
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• Vortex-Peierls States in Optical Lattices
• Interacting Hofstadter spectrum of atoms in an artificial gauge field
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Cited by in corpus (4)

• Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
• Signatures of many-body localization of quasiparticles in a flat band superconductor
• Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $\pi$-flux Dice Lattice with Flat Bands
• Quantum Rotor Theory of Systems of Spin-2 Bosons