The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields

Abstract

We derive the reciprocal cluster mean-field method to study the strongly-interacting bosonic Harper-Hofstadter-Mott model. The system exhibits a rich phase diagram featuring band insulating, striped superfluid, and supersolid phases. Furthermore, for finite hopping anisotropy we observe gapless uncondensed liquid phases at integer fillings, which are analyzed by exact diagonalization. The liquid phases at fillings 1 and 3 exhibit the same band fillings as the fermionic integer quantum Hall effect, while the phase at filling 2 is CT-symmetric with zero charge response. We discuss how these phases become gapped on a quasi-one-dimensional cylinder, leading to a quantized Hall response, which we characterize by introducing a suitable measure for non-trivial many-body topological properties. Incompressible metastable states at fractional filling are also observed, indicating competing fractional quantum Hall phases. The combination of reciprocal cluster mean-field and exact diagonalization yields a promising method to analyze the properties of bosonic lattice systems with non-trivial unit cells in the thermodynamic limit.

16 pages, 11 figures

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Cited by in corpus (18)

• Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Charge excitation dynamics in bosonic fractional Chern insulators
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Bosonic quantum Hall states in single-layer two-dimensional optical lattices
• Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics
• Finite-temperature properties of interacting bosons on a two-leg flux ladder
• 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
• Exploring helical phases of matter in bosonic ladders
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Topological Supersolidity of Dipolar Fermi Gases in a Spin-Dependent Optical Lattice
• Extended Bose-Hubbard models with Rydberg macrodimer dressing
• Detecting Hidden Order in Fractional Chern Insulators
• Quasi-one-dimensional Hall physics in the Harper-Hofstadter-Mott model
• Quantum Hall states for $\alpha =1/3$ in optical lattices
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code