Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

Abstract

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\pi$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising it pairs of bosons. Interestingly, the high- and low- density regions have an overlap, where the two phases coexist.

6 pages, 4 figures

References in corpus (9)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Bose condensation in flat bands
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Topology induced anomalous defect production by crossing a quantum critical point
• Exact many-electron ground states on the diamond Hubbard chain
• Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase Separation and Luttinger Liquid Behavior

Cited by in corpus (67)

• Artificial flat band systems: from lattice models to experiments
• Geometric origin of superfluidity in the Lieb lattice flat band
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Preformed pairs in flat Bloch bands
• Geometry induced pair condensation
• Flat-band many-body localization and ergodicity breaking in the Creutz ladder
• Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing
• Pairing and superconductivity in the flat band: Creutz lattice
• Topology and interactions in the photonic Creutz and Creutz-Hubbard ladders
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Nonlinear dynamics of Aharonov-Bohm cages
• Nonlinear caging in All-Bands-Flat Lattices
• New class of flat-band models on tetragonal and hexagonal lattices: Gapped versus crossing flat bands
• Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Interaction-induced topological properties of two bosons in flat-band systems
• Nonlinear symmetry breaking of Aharonov-Bohm cages
• Electron-Phonon Interactions in Flat Band Systems
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Flat bands and long range Coulomb interactions: conducting or insulating?
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Systematic construction of topological flat-band models by molecular-orbital representation
• Fast quantum transfer mediated by topological domain walls
• Strain induced superconductor-insulator transition on Lieb lattice
• Many-body Aharonov-Bohm caging in a lattice of rings
• Low-energy behaviour of strongly-interacting bosons on a flat-banded lattice above the critical filling factor
• Quantum diffusion and thermalization at resonant tunneling
• Haldane phase in the sawtooth lattice: Edge states, entanglement spectrum and the flat band
• Superfluid weight in the isolated band limit within the generalized random phase approximation
• The Rhombi-Chain Bose-Hubbard Model: geometric frustration and interactions
• Floquet-engineered nonlinearities and controllable pair-hopping processes: From optical Kerr cavities to correlated quantum matter
• Floquet engineering of optical nonlinearities: a quantum many-body approach
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Isolated flat bands in an interlocking-circles lattice
• Frustration-induced supersolids in the absence of inter-site interactions
• Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder
• Drude weight and the many-body quantum metric in one-dimensional Bose systems
• Interacting bosons in two-dimensional flat band systems
• Magnetic and nonmagnetic phases in doped AB2 t-J Hubbard chains
• Topological chiral currents in the Gross-Neveu model extension
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Localization of Rung Pairs in Hard-core Bose-Hubbard Ladder
• Nematic quantum liquid crystals of bosons in frustrated lattices
• Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions
• Spectral Properties of Two Coupled Fibonacci Chains
• Pair formation of hard core bosons in flat band systems
• Hubbard models and state preparation in an optical Lieb lattice
• Interaction-induced conductance from zero modes in a clean magnetic graphene waveguide
• Critical States Generators from Perturbed Flatbands
• Superconducting pairing from repulsive interactions of fermions in a flat-band system
• Fractional charge and emergent mass hierarchy in diagonal two-leg t-J cylinders
• Three-body interacting dipolar bosons and the fate of lattice supersolidity
• Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons with a Flat Band
• Quantum phases of constrained bosons on a two-leg Bose-Hubbard ladder
• Hard-core bosons in flat band systems above the critical density
• Superfluidity from correlations in driven boson systems
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Dissipation-Induced Mobility and Coherence in Frustrated Lattices
• Topological bosonic states on ribbons of honeycomb lattice
• Coexistence of ergodic and non-ergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor
• Chaotic level mixing in a two-band Bose-Hubbard model
• Many-body phases from effective geometrical frustration and long-range interactions in a subwavelength lattice
• Fate of chiral order and impurity self-pinning in flat bands with local symmetry
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Controlling correlations of a polaritonic Luttinger liquid by engineered cross-Kerr nonlinearity