Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Abstract

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

Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

“…The chiral MI ground state thus supports a staggered (antiferromagnetic) angular momentum pattern, with a non-zero order parameter L stag z ðrÞ ¼ ð À 1Þ rx þ ry L z ðrÞ out to arbitrarily strong coupling. Such staggered time-reversal symmetry broken MIs, albeit for far more delicate plaquette currents, are known to emerge in frustrated Bose Hubbard models without orbital degrees of freedom, but only in an extremely small parameter window of interactions [39][40][41] . As schematically shown in Fig.…”

Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

“…Bosons on a ladder subjected to gauge fields have been the topic of previous theoretical work [37][38][39][40][41][42][43][44] (see also [45,46] for 2D lattices), yet complete quantitative phase diagrams are lacking. In our work, we use DMRG to systematically explore the full dependence on J ⊥ , φ, and filling and, as a main result, we observe both gapped and gapless Meissner and vortex phases for stronglyinteracting bosons.…”

Supersolid in a one-dimensional model of hard-core bosons

“…On the other hand, the ability to produce frustration in optical lattices of cold atoms has opened up possibilities to realize interesting superfluid and Mott states which have additional kinds of order arising from the kinetic frustration [22][23][24]. Kinetic frustration in these systems is produced by the competition of two different hopping processes from a site to different sites with different signs of the hopping amplitude.…”