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 examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equations clearly show that a formally time-reversible system is able to reproduce the features of a 2D turbulent flow. Statistical quantities based on one-and two-point measurements show an excellent agreement between the two systems, for the inverse-and direct cascade regions. Moreover, we find that the conjecture holds very well for 2D turbulent flows with both conserved energy and enstrophy at finite Reynolds number, which goes beyond the original conjecture for three-dimensional turbulence in the limit of infinite Reynolds number.

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