Fermionization of Bosons in a Flat Band

Abstract

Strongly interacting bosons that live in a lattice with degeneracy in its lowest energy band experience frustration that can prevent the formation of a Bose-Einstein condensate. Such systems form an ideal playground to investigate spin-liquid behavior. We use the variational principle and the Chern-Simons technique of fermionization of hard-core bosons on Kagome lattice to find that below lattice filling fraction $\nu =1/3$ the system favors a topologically ordered chiral spin-liquid state that is gapped in bulk, spontaneously breaks Time-Reversal Symmetry, and supports massless chiral bosonic edge mode. We construct the many-body variational wave function of the state and show that the corresponding energy coincides with the energy of the flat band. This result proves that the ground state of the system cannot stabilize a Bose condensate below $\nu =1/3$. The fermionization and variational scheme we outline apply to any non-Bravais lattice. We distinguish between the roles played by the Chern-Simons gauge field in lattices with a flat band and those exhibiting a moat-like dispersion (which is degenerate along a closed contour in the reciprocal space). We also suggest experimental probes to differentiate the proposed ground state from a condensate.

arXiv comment11 pages, Revtex, 6 figures

References in corpus (42)

• Anyons in an exactly solved model and beyond
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Topological orders and Edge excitations in FQH states
• Bragg spectroscopy of a Bose-Einstein condensate
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Observation of the Meissner effect with ultracold atoms in bosonic ladders
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Ultracold Atoms in a Tunable Optical Kagome Lattice
• Band touching from real space topology in frustrated hopping models
• An exact chiral spin liquid with non-Abelian anyons
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Bose condensation in flat bands
• Momentum-Resolved Bragg Spectroscopy in Optical Lattices
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• The kagome antiferromagnet: a chiral topological spin liquid ?
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices
• Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Projective symmetry group classification of chiral spin liquids
• Gapless chiral spin liquid in a kagome Heisenberg model
• Bragg Spectroscopy of ultracold atoms loaded in an optical lattice
• Composite fermion state of spin-orbit coupled bosons
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Chiral spin liquids on the kagome Lattice
• Absence of Bose condensation on lattices with moat bands
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
• Statistical transmutation in Floquet driven optical lattices
• Chern-Simons Composite Fermion Theory of Fractional Chern Insulators
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Topological spin ordering via Chern-Simons superconductivity
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Signatures of fractionalization in spin liquids from interlayer thermal transport
• Antiferromagnetic magnons from fractionalized excitations
• D-wave superconductivity induced by proximity to the non-uniform chiral spin liquid on a square lattice

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• Chiral spin liquid state of strongly interacting bosons with a moat dispersion: a Monte Carlo simulation
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• Cavity-Vacuum-Induced Chiral Spin Liquids in Kagome Lattices: Tuning and Probing Topological Quantum Phases via Cavity Quantum Electrodynamics
• Trapping Hard-Core Bosons in Flatband Lattices
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• Partial quantum revivals of localized condensates in distorted lattices
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Correlated phases of moat-band excitons in two dimensions