Composite Fermion Theory for Bosonic Atoms in Optical Lattices

Abstract

We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial wavefunctions for these phases, and perform numerical tests of the predictions of the composite fermion model. Our results establish the existence of strongly correlated phases beyond those in the continuum limit, and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau-level.

arXiv comment4 pages, 2 figures

References in corpus (22)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
• Rapidly Rotating Atomic Gases
• Fractional quantum Hall states of atoms in optical Lattices
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level
• Fractional Quantum Hall Effect in Optical Lattices
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Do attractive bosons condense?
• Observation of Vortex Pinning in Bose-Einstein Condensates
• Quantum Hall fractions in rotating Bose-Einstein condensates
• Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids
• High field fractional quantum Hall effect in optical lattices
• A Composite Fermion Description of Rotating Bose-Einstein Condensates
• A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet
• Optical lattice quantum Hall effect
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice
• Hall effects in Bose-Einstein condensates in a rotating optical lattice
• Vortex lattices of bosons in deep rotating optical lattices
• Uniformly frustrated bosonic Josephson-junction arrays
• Competing Compressible and Incompressible Phases in Rotating Atomic Bose Gases at Filling Factor $\nu =2$

Cited by in corpus (140)

• Artificial gauge potentials for neutral atoms
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Topological Bands for Ultracold Atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Fractional Chern Insulator
• Topological Flat Band Models and Fractional Chern Insulators
• Fractional Quantum Hall Physics in Topological Flat Bands
• Topological quantum matter with cold atoms
• Gauge fields for ultracold atoms in optical superlattices
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Optical Flux Lattices for Ultracold Atomic Gases
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
• Fractional Chern Insulators and the W-Infinity Algebra
• Realization of a fractional quantum Hall state with ultracold atoms
• Periodically-driven quantum matter: the case of resonant modulations
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Geometric stability of topological lattice phases
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Bosonic Mott Insulator with Meissner Currents
• Correlated phases of bosons in the flat lowest band of the dice lattice
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• A continuous transition between fractional quantum Hall and superfluid states
• Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices
• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Theory of Bosons in two-leg ladders with large magnetic fields
• Bosonic Integer Quantum Hall effect in an interacting lattice model
• A discretized Chern-Simons gauge theory on arbitrary graphs
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Fractional Chern Insulators beyond Laughlin states
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Topological bands with Chern number C=2 by dipolar exchange interactions
• Adiabatic continuity between Hofstadter and Chern insulator states
• Condensed Groundstates of Frustrated Bose-Hubbard Models
• Many-body Chern number without integration
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Mott transition in a two-leg Bose-Hubbard ladder under an artificial magnetic field
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Hamiltonian theory of fractionally filled Chern bands
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux
• Bosonic integer quantum Hall effect in optical flux lattices
• Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Fractional Chern Insulators from the nth Root of Bandstructure
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Photon-Assisted-Tunneling Toolbox for Quantum Simulations in Ion Traps
• Model Fractional Chern Insulators
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux
• Three-level Haldane-like model on dice optical lattice
• Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• Edge excitations of bosonic fractional quantum Hall phases in optical lattices
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Charge excitation dynamics in bosonic fractional Chern insulators
• Bosonic Fractional Quantum Hall States on a Finite Cylinder
• Characterization of quasiholes in fractional Chern insulators
• Wigner crystallization in topological flat bands
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Quantum Simulation Architecture for Lattice Bosons in Arbitrary, Tunable External Gauge Fields
• Fractional Quantum Hall states in the vicinity of Mott plateaus
• Chern-Simons Composite Fermion Theory of Fractional Chern Insulators
• Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions
• Pairing and Vortex Lattices for Interacting Fermions in Optical Lattices with a Large Magnetic Field
• The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Bosonic Analogs of Fractional Quantum Hall State in the Vicinity of Mott States
• Interacting bosons in topological optical flux lattices
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Creating a bosonic fractional quantum Hall state by pairing fermions
• Local tensor network for strongly correlated projective states
• Static and Dynamic Properties of Interacting Spin-1 Bosons in an Optical Lattice
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles
• Bosonic integer quantum Hall states in topological bands with Chern number two
• Dissipative preparation of fractional Chern insulators
• Realization of strongly-interacting Meissner phases in large bosonic flux ladders
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model
• Phase diagrams of Bose-Hubbard model and Haldane-Bose-Hubbard model with complex hopping amplitudes
• Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
• Parafermionic zero modes in ultracold bosonic systems
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Competing orders in the Hofstadter t-J model
• Josephson Coupled Moore-Read States
• Bosonic integer quantum Hall effect as topological pumping
• Adiabatic continuity, wavefunction overlap and topological phase transitions
• Landau Levels in Lattices with Long Range Hopping
• Multi-faceted machine learning of competing orders in disordered interacting systems
• Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge
• Quantum phases of strongly-interacting bosons on a two-leg Haldane ladder
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Lattice realization of a bosonic integer quantum Hall state - trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Model wavefunctions for interfaces between lattice Laughlin states
• Broken Symmetry in Ideal Chern Bands
• Degeneracy of Many-body Quantum States in an Optical Lattice with a Uniform Magnetic Field
• Variational identification of a fractional Chern insulator in an extended Bose-Hubbard model
• Growing quantum states with topological order
• Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
• Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $\pi$-flux Dice Lattice with Flat Bands
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field
• Universality and quantized response in bosonic nonfractionalized tunneling
• Parafermions in Moiré Minibands
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
• Detecting Hidden Order in Fractional Chern Insulators
• Quasi-one-dimensional Hall physics in the Harper-Hofstadter-Mott model
• Interaction-driven plateau transition between integer and fractional Chern Insulators
• Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
• On the geometrical description of fractional Chern insulators based on static structure factor calculations
• Probing Quantum Anomalous Hall States in Twisted Bilayer WSe2 via Attractive Polaron Spectroscopy
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• Topological Order Without Band Topology in Moiré Graphene
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• Chiral Edge Excitations of $\nu =1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model