We study two-component bosons on the Harper-Hofstadter model with two legs. The synthetic magnetic fields for the two types of bosons point to either the same direction or opposite directions. The bosons have hardcore intraspecies interaction such that there can be no more than one boson of the same type on each lattice site. For certain filling factors in the absence of interspecies interaction, each component realizes a vortex Mott insulator with rung current or a Meissner superfluid without rung current. The system undergoes phase transitions to other phases as interspecies interaction is turned on, which are characterized numerically using the density matrix renormalization group method and supplemented with analytical studies when possible. The vortex Mott insulator transits to a gapped Meissner phase without rung current and the Meissner superfluid transits to a gapped vortex phase with rung current. In both cases, we observe gapped spin density wave states that break certain ${\mathbb{Z}}_{2}$ symmetries.
We study two-component bosons on the Harper-Hofstadter model with two legs. The synthetic magnetic fields for the two types of bosons point to either the same direction or opposite directions. The bosons have hardcore intraspecies interaction such that there can be no more than one boson of the same type on each lattice site. For certain filling factors in the absence of interspecies interaction, each component realizes a vortex Mott insulator with rung current or a Meissner superfluid without rung current. The system undergoes phase transitions to other phases as interspecies interaction is turned on, which are characterized numerically using the density matrix renormalization group method and supplemented with analytical studies when possible. The vortex Mott insulator transits to a gapped Meissner phase without rung current and the Meissner superfluid transits to a gapped vortex phase with rung current. In both cases, we observe gapped spin density wave states that break certain Z2 symmetries.
Bosons in periodic potentials with very strong local interactions, known as constrained bosons, often exhibit interesting physical behavior. We investigate the ground-state properties of a two-leg Bose-Hubbard ladder by imposing a three-body constraint in one leg and a hard-core constraint in the other. By using the cluster mean-field theory approximation and the density matrix renormalization group method, we show that at unit filling, for strong two-body attraction among the three-body constrained bosons, the system becomes a gapped pair-Mott insulator where all the bosons form strong bound pairs and occupy the leg with the three-body constraint. With increase in hopping strength, this pair-Mott insulator phase undergoes a phase transition to the gapless superfluid phase for equal leg and rung hopping strengths. However, when the rung hopping is stronger compared to the leg hopping, we obtain a crossover to another gapped phase which is called the rung-Mott insulator phase where the bosons prefer to delocalize on the rungs rather than the legs. By moving away from unit filling, the system remains in the superfluid phase except for a small region below the gapped phase where a pair superfluid phase is stabilized in the regime of strong attractive interaction. We further extend our studies by considering the three-body constraint in both the legs and find that the crossover from the gapped to gapped phase does not occur; rather, the system undergoes a transition from a pair-rung-Mott insulator phase to the superfluid phase at unit filling. Moreover, in this case, we find the signature of the pair superfluid phase on either side of this gapped phase.
We introduce generic bosonic models exemplifying that chiral Meissner currents can persist in insulating phases of matter. We first consider interacting bosons on a two-leg ladder. The total density sector can be gapped in a bosonic Mott insulator at odd-integer filling, while the relative density sector remains superfluid due to interchain hopping. Coupling the relative density to gauge fields yields a pseudospin Meissner effect. We show that the same phase arises if the bosons are replaced by spinful fermions confined in Cooper pairs, and find a dual fermionic Mott insulator with spinon currents. We prove that, by tuning the mean density, the Mott insulator with Meissner currents turns into a low-dimensional bosonic $\ensuremath{\nu}=\frac{1}{2}$ Laughlin state for strong enough repulsive interactions across the ladder rungs. We finally discuss extensions to multileg ladders and bilayers in which spinon superfluids with Meissner currents become possible. We propose two experimental realizations, one with ultracold atoms in the setup of Atala et al. [Nat. Phys. 10, 588 (2014)] and another with Josephson junction arrays. We also address a Bose-Fermi mixture subject to a magnetic field in connection with the pseudogap phase of high-Tc cuprates.
We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.
A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is ρπ and close to it, where ρ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung–rung correlation function and the spin–spin and charge–charge static structure factors.
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.
We establish the phase diagram of the strongly interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [M. Atala et al., Nat. Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, interleg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.