We consider a Bose–Hubbard ladder subject to an artificial magnetic flux and discuss its different ground states, their physical properties, and the quantum phase transitions between them. A low-energy effective field theory is derived, in the two distinct regimes of a small and large magnetic flux, using a bosonization technique starting from the weak-coupling limit. Based on this effective field theory, the ground-state phase diagram at a filling of one particle per site is investigated for a small flux and for a flux equal to π per plaquette. For π -flux, this analysis reveals a tricritical point, which has been overlooked in previous studies. In addition, the Mott insulating state at a small magnetic flux is found to display Meissner currents.
Abstract We investigate the ground state properties of interacting bosons on a triangular ladder subject to an artificial magnetic field. By means of the mean-field approximation, rich phases are revealed in the limit of weak interaction and large bosons occupation per site, including the Meissner superfluid, vortex superfluid, biased chiral superfluid (C-SF), C-SF and insulating phases. The quantum phases can be precisely identified and the underlying physics of phase transitions can be clarified by utilizing order parameters based on the atomic density, the effective rung current, and the current asymmetry ratio. Meanwhile, the phase transition of the system can be effectively controlled by adjusting the rung-to-leg coupling ratio, the magnetic flux and the atomic interaction. Furthermore, using Bogoliubov theory, we have mapped the stability phase diagram across all parameters, and clarified the interdependence between superfluidity and the dispersion relation. The excitation spectrum, which effectively describes the system’s energetic stability, is governed by the rung-to-leg coupling ratio, the magnetic flux, and the atomic interaction. Numerical simulations validate the dynamical instability of the system. This work offers a theoretical foundation for identifying new quantum phases exhibited by ultracold atoms in optical lattices and new experimental approaches for achieving system superfluidity.
We consider the Bose-Hubbard model on a two-leg ladder under an artificial magnetic field and investigate the superfluid--to--Mott insulator transition in this setting. Recently, this system has been experimentally realized [M. Atala et al., Nature Phys. 10, 588 (2014)], albeit in a parameter regime that is far from the Mott transition boundary. Depending on the strength of the magnetic field, the single-particle spectrum has either a single ground state or two degenerate ground states. The transition between these two phases is reflected in the many-particle properties. We first investigate these phases through the Bogoliubov approximation in the superfluid regime and calculate the transition boundary for weak interactions. For stronger interactions the system is expected to form a Mott insulator. We calculate the Mott transition boundary as a function of the magnetic field and interleg coupling with mean-field theory, strong-coupling expansion, and density matrix renormalization group (DMRG). Finally, using the DMRG, we investigate the particle-hole excitation gaps of this system at different filling factors and find peaks at simple fractions, indicating the possibility of correlated phases.
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 model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-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.
We explore the behavior of the Hall response of a Bose-Hubbard triangular ladder in a magnetic field as a function of the repulsive on-site atomic interactions. We consider a wide range of interaction strengths, from the weakly interacting limit to the hard-core regime. This is realized by computing the Hall polarization following the quench of a weak linear potential, which induces the flow of a current through the system, using time-dependent matrix product state numerical simulations. We complement our understanding in the regime of small magnetic fields by analytical calculations of the equilibrium value of the Hall polarization for noninteracting bosonic atoms and under a mean-field assumption. The Bose-Hubbard triangular flux ladder exhibits a rich phase diagram, containing Meissner, vortex, and biased-chiral, superfluid phases. We show that the Hall response can be employed to fingerprint the various chiral states, the frustration effects occurring in the limit of strong interactions, and the phase boundaries of the equilibrium phase diagram.
We investigate the ground-state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex-antivortex configuration. The analytical results are confirmed by numerical simulations using a cluster mean-field-theory approach.
We investigate the ground-state phase diagram of repulsively interacting bosons on a two-leg ladder threaded by a uniform artificial magnetic flux, using the cluster Gutzwiller mean-field method. In the strong-rung-coupling regime, self-consistent calculations are performed on a
2×4 cluster. By analyzing the superfluid order parameter, leg-resolved currents, chiral current, the current ratio on adjacent legs, and the density imbalance between the two legs, we distinguish Mott-insulating from superfluid regimes and characterize the observed states as Meissner-like, vortex-like (superfluid or Mott insulating), or biased-ladder. In regions overlapping with previous DMRG studies, our results qualitatively agree with the established phase structure, demonstrating that the cluster Gutzwiller approach balances computational efficiency and physical accuracy. We then construct the first grand-canonical
t--
μ phase diagrams for this system, revealing how the magnetic flux modifies the shape, tilt, and extent of the Mott lobes. We further explore previously inaccessible regimes, including higher fillings
ρ≳1 and the intermediate interaction window
U/t∈[7.69,9.09]. Special attention is paid to
φ=π, where the effective triangular-ladder mapping becomes singular. Owing to the equivalence of
φ=π and
−π modulo
2π, a combined symmetry forbids net chiral currents, leading to a nonchiral Mott-insulating state, in contrast to the chiral-superfluid tendency expected away from
φ=π. Our results offer a computationally efficient route for mapping the global phase structure of bosonic flux ladders and provide guidance for future ultracold-atom experiments in artificial gauge fields.