Correlated Phases in Bose-Hubbard Models with Simulated Magnetic Fields

Beibing Huang, Shaolong Wan

J. H. Pixley, William S. Cole, Matteo Rizzi +1 more

Arun Paramekanti, Maheswar Maji, Arya Dhar +3 more

Sagarika Basak, Han Pu

Yoshihito Kuno, Takashi Nakafuji, Ikuo Ichinose

In this paper, we study Bose-Hubbard models on square and honeycomb lattices with complex hopping amplitudes, which are feasible by recent experiments of cold atomic gases in optical lattices. To clarify phase diagrams, we use extended quantum Monte Carlo simulations (eQMC). For the system on the square lattice, the complex hopping is realized by an artificial magnetic field. We found that vortex-solid states form for certain set of magnetic field, i.e., the magnetic field with the flux quanta per plaquette $f=p/q$, where $p$ and $q$ are co-prime natural numbers. For the system on the honeycomb lattice, we add the next-nearest-neighbor complex hopping. The model is a bosonic analog of the Haldane-Hubbard model. By means of eQMC, we study the model with both weak and strong onsite repulsions. Numerical study shows that the model has a rich phase diagram. We also found that in the system defined on the honeycomb lattice of the cylinder geometry, an interesting edge state appears.

Arya Dhar, Tapan Mishra, Maheswar Maji +3 more

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum $\mathrm{XY}$ model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.