Competing ground states of strongly correlated bosons in the Harper-Hofstadter-Mott model

Abstract

Using an efficient cluster approach, we study the physics of two-dimensional lattice bosons in a strong magnetic field in the regime where the tunneling is much weaker than the on-site interaction strength. We study both dilute, hard core bosons at filling factors much smaller than unity occupation per site, and the physics in the vicinity of the superfluid-Mott lobes as the density is tuned away from unity. For hardcore bosons, we carry out extensive numerics for a fixed flux per plaquette $\varphi =1/5$ and $\varphi =1/3$. At large flux, the lowest energy state is a strongly correlated superfluid, analogous to He-$4$, in which the order parameter is dramatically suppressed, but non-zero. At filling factors $\nu =1/2,1$, we find competing incompressible states which are metastable. These appear to be commensurate density wave states. For small flux, the situation is reversed, and the ground state at $\nu =1/2$ is an incompressible density-wave solid. Here, we find a metastable lattice supersolid phase, where superfluidity and density-wave order coexist. We then perform careful numerical studies of the physics near the vicinity of the Mott lobes for $\varphi =1/2$ and $\varphi =1/4$. At $\varphi =1/2$, the superfluid ground state has commensurate density-wave order. At $\varphi =1/4$, incompressible phases appear outside the Mott lobes at densities $n=1.125$ and $n=1.25$, corresponding to filling fractions $\nu =1/2$ and $1$ respectively. These phases, which are absent in single-site mean-field theory are metastable, and have slightly higher energy than the superfluid, but the energy difference between them shrinks rapidly with increasing cluster size, suggestive of an incompressible ground state. We thus explore the interplay between Mott physics, magnetic Landau levels, and superfluidity, finding a rich phase diagram of competing compressible and incompressible states.

10 pages, 6 figures. Comments are welcome

References in corpus (18)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Fractional Quantum Hall Effect in Optical Lattices
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Half-Filled Lowest Landau Level on a Thin Torus
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Phases of a 2D Bose Gas in an Optical Lattice
• Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Interacting Hofstadter spectrum of atoms in an artificial gauge field

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• Bosonic quantum Hall states in single-layer two-dimensional optical lattices
• 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
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Extended Bose-Hubbard models with Rydberg macrodimer dressing
• Laser assisted tunneling in a Tonks-Girardeau gas
• Quantum Hall states for $\alpha =1/3$ in optical lattices
• Vortex core ordering in Abrikosov lattices
• 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
• Finite size effects and Hofstadter butterfly in a bosonic Mott insulator with relativistic dispersion background
• Theory of Hofstadter Superconductors