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.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.

arXiv:1207.1725Physical Review BMay 3, 2013113 citations

Variational Study on Loop Currents in Bose Hubbard model with Staggered Flux

Yuta Toga, H. Yokoyama

In view of strongly interacting bosons in an optical lattice with a large gauge field, we study phase transitions in a two-dimensional Bose-Hubbard model with a staggered flux, on the basis of variational Monte Carlo calculations. Inthe trial states,besides typical onsite and intersite correlation factors, we introduce a configuration-dependent phase factor,which was recently found essential for treating current-carrying states. It is found that this phase factor is qualitativelyvitalfordescribing a Mott insulating (MI) state in the present model. Thereby, the Peierls phasesattached in relevant hopping processes are cancelled out. As a result, local currents completely suppressed in MI states, namely, a chiral Mott state does not appear for the square lattice, in contrast tothecorresponding two-leg ladder model. In addition, we discuss other features of the first-order superfluid-MI transition in this model.In view of strongly interacting bosons in an optical lattice with a large gauge field, we study phase transitions in a two-dimensional Bose-Hubbard model with a staggered flux, on the basis of variational Monte Carlo calculations. Inthe trial states,besides typical onsite and intersite correlation factors, we introduce a configuration-dependent phase factor,which was recently found essential for treating current-carrying states. It is found that this phase factor is qualitativelyvitalfordescribing a Mott insulating (MI) state in the present model. Thereby, the Peierls phasesattached in relevant hopping processes are cancelled out. As a result, local currents completely suppressed in MI states, namely, a chiral Mott state does not appear for the square lattice, in contrast tothecorresponding two-leg ladder model. In addition, we discuss other features of the first-order superfluid-MI transition in this model.

Physics ProcediaJan 1, 20153 citations

Chiral Mott insulator of kinetically frustrated bosons

Arun Paramekanti, Arya Dhar, Maheswar Maji +3 more

Bulletin of the American Physical SocietyFeb 29, 20120 citations

The superfluid-Mott insulator transition in 2D

Ian B. Spielman, J. H. Huckans, Jennifer Sebby-Strabley +4 more

Bulletin of the American Physical SocietyMar 16, 20060 citations

Artificial staggered magnetic field for ultracold atoms in optical lattices

Lih-King Lim, Andreas Hemmerich, C. Morais Smith

A time-dependent optical lattice with staggered particle current in the tight-binding regime was considered that can be described by a time-independent effective lattice model with an artificial staggered magnetic field. The low-energy description of a single-component fermion in this lattice at half-filling is provided by two copies of ideal two-dimensional massless Dirac fermions. The Dirac cones are generally anisotropic and can be tuned by the external staggered flux $\ensuremath{\phi}$. For bosons, the staggered flux modifies the single-particle spectrum such that in the weak coupling limit, depending on the flux $\ensuremath{\phi}$, distinct superfluid phases are realized. Their properties are discussed, the nature of the phase transitions between them is established, and Bogoliubov theory is used to determine their excitation spectra. Then the generalized superfluid--Mott-insulator transition is studied in the presence of the staggered flux and the complete phase diagram is established. Finally, the momentum distribution of the distinct superfluid phases is obtained, which provides a clear experimental signature of each phase in ballistic expansion experiments.A time-dependent optical lattice with staggered particle current in the tight-binding regime was considered that can be described by a time-independent effective lattice model with an artificial staggered magnetic field. The low-energy description of a single-component fermion in this lattice at half-filling is provided by two copies of ideal two-dimensional massless Dirac fermions. The Dirac cones are generally anisotropic and can be tuned by the external staggered flux $\ensuremath{\phi}$. For bosons, the staggered flux modifies the single-particle spectrum such that in the weak coupling limit, depending on the flux $\ensuremath{\phi}$, distinct superfluid phases are realized. Their properties are discussed, the nature of the phase transitions between them is established, and Bogoliubov theory is used to determine their excitation spectra. Then the generalized superfluid--Mott-insulator transition is studied in the presence of the staggered flux and the complete phase diagram is established. Finally, the momentum distribution of the distinct superfluid phases is obtained, which provides a clear experimental signature of each phase in ballistic expansion experiments.

arXiv:0910.2610Physical Review AFeb 4, 201061 citations

\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.