Description
We derive the reciprocal cluster mean-field method to study
the strongly-interacting bosonic Harper-Hofstadter-Mott
model. In terms of the hopping anisotropy and the chemical
potential, the system exhibits a rich phase diagram featuring
band insulating, striped superfluid, and supersolid phases.
Furthermore, for finite anisotropy we observe gapless
uncondensed liquid phases at integer fillings, which are
analyzed by exact diagonalization. The liquid phases at
fillings ? = 1, 3 exhibit the same band fillings as the fermionic
integer quantum Hall effect, while the phase at ? = 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 is characterized
by 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.
