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Motivated by experiments on Josephson junction arrays in a magnetic field andultracold interacting atoms in an optical lattice in the presence of syntheticorbital magnetic fields, we study the "fully frustrated" Bose-Hubbard model andquantum XY model with half a flux quantum per lattice plaquette. Using MonteCarlo simulations and the density matrix renormalization group (DMRG) method,we show that the phase diagram of such kinetically frustrated bosons displaysthree phases on a two-leg ladder: a weakly interacting chiral superfluid phasewith staggered loop currents which spontaneously break time-reversal symmetry,a conventional Mott insulator at strong coupling, and a remarkable "Chiral MottInsulator" (CMI) with staggered loop currents sandwiched between them atintermediate correlation. We discuss how the CMI state may be viewed as anexciton condensate or a vortex supersolid, propose and study a Jastrowvariational wavefunction which captures its correlations, present DMRG resultsfor the boson momentum distribution across the phase diagram, and considervarious experimental implications of our phase diagram. Finally, we discussgeneralizations to a staggered flux Bose-Hubbard model and a two-dimensionalversion of the CMI with edge currents in weakly coupled ladders.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose Hubbard model