Fractional Quantum Hall states in the vicinity of Mott plateaus

Abstract

We perform variational Monte-Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one-another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground-state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.

6 pages, 4 figures

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Cited by in corpus (23)

• Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Condensed Groundstates of Frustrated Bose-Hubbard Models
• Single-site-resolved measurement of the current statistics in optical lattices
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Quantum Simulation Architecture for Lattice Bosons in Arbitrary, Tunable External Gauge Fields
• Bosonic quantum Hall states in single-layer two-dimensional optical lattices
• Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions
• The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields
• Bosonic Analogs of Fractional Quantum Hall State in the Vicinity of Mott States
• Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Landau Levels in Lattices with Long Range Hopping
• Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux
• BCS theory of time-reversal-symmetric Hofstadter-Hubbard model
• Degeneracy of Many-body Quantum States in an Optical Lattice with a Uniform Magnetic Field
• Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field
• Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
• Quasi-one-dimensional Hall physics in the Harper-Hofstadter-Mott model
• The influence of sublattice bias on superfluid to Mott insulator transitions
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• Quantum Hall states for $\alpha =1/3$ in optical lattices
• Finite size effects and Hofstadter butterfly in a bosonic Mott insulator with relativistic dispersion background