Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the "fully frustrated" Bose-Hubbard (FFBH) model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a 2-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.The simplest model to understand strongly correlated bosons is the Bose-Hubbard (BH) model [1] which describes bosons hopping on a lattice and interacting via a local repulsive interaction. With increasing repulsion, at integer filling, its ground state undergoes a superfluid to Mott insulator quantum phase transition which has been studied using ultracold atoms in an optical lattice [2].Remarkably, recent experiments have used two-photon Raman transitions to create a uniform or staggered "synthetic magnetic field" for neutral atoms [3], permitting one to access large magnetic fields for lattice bosons. The multiple degenerate minima in the resulting Hofstadter spectrum can be populated by non-interacting bosons in many ways. Repulsive interactions quench this "kinetic frustration", leading to unconventional superfluids [4][5][6][7], or quantum Hall liquids [8]. Tuning the sign of the atom hopping amplitude or populating higher bands also leads to such frustrated bosonic fluids [4]. These developments motivate us to study the interplay of strong correlations and frustration in the fully frustrated BoseHubbard (FFBH), with half a "magnetic flux" quantum per plaquette [5][6][7]. At large integer filling, the FFBH is also the simplest quantum variant of the classical fully frustrated XY (FFXY) model [9, 10] of Josephson junction arrays (JJAs) [11].Here, we obtain the phase diagram shown in Fig. 1 of the FFBH model at integer filling on a 2-leg ladder using the density matrix renormalization group (DMRG) method [12] and Monte Carlo (MC) simulations. Our key result is that the ground state of the FFBH and quantum FFXY models at intermediate Hubbard repulsion is a chiral Mott Insulator (CMI). The CMI has a nonzero charge gap, and simultaneously supports staggered loop currents that spontaneously break time reversal symmetry. With increasing repulsion, the CMI undergoes an Ising transition into an ordinary Mott insulator (MI) where the loop currents vanish. Weakening the repulsion leads to a Berezinskii-Kosterlitz-Thouless (BKT) [13] transition out of the CMI into a previously studied

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 fields, we study the "fully frustrated" Bose-Hubbard model and quantum 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 wavefunction 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.

We study the phase diagram of spinless fermions with nearest-and next-nearest-neighbor interactions in one dimension utilizing the (finite-size) density-matrix renormalization group method. The competition between nearest-and next-nearest-neighbor interactions and nearest-neighbor hopping generates four phases in this model: two charge-density-wave insulators, a Luttinger-liquid phase, and a bond-order phase. We use finite-size scaling of the gap and various structure factors to determine the phase diagram.

We obtain the ground-state quantum phase diagram for a two-species Bose mixture in a one-dimensional optical lattice using the finite-size density-matrix renormalization group method. We discuss our results for different combinations of inter-and intraspecies interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are a superfluid and a Mott insulator, and a phase separation where the two different species reside in spatially separate regions. The spatially separated phase is further classified into phase-separated superfluid and Mott insulator. The phase separation appears for all the fillings we have considered, whenever the interspecies interaction is slightly larger than the intraspecies interactions.