Marie Piraud

Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: swimming against the tide

The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While noninteracting as well as strongly interacting particles, stirred by the magnetic field, circulate along the systems boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.

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

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.

Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: A density-matrix renormalization-group study

In this paper, we provide a comprehensive study of the quantum magnetism in the Mott insulating phases of the one-dimensional (1D) Bose-Hubbard model with Abelian or non-Abelian synthetic gauge fields, using the density-matrix renormalization-group (DMRG) method. We focus on the interplay between the synthetic gauge field and the asymmetry of the interactions, which give rise to a very general effective magnetic model: an XYZ model with various Dzyaloshinskii-Moriya (DM) interactions. The properties of the different quantum magnetic phases and phases transitions of this model are investigated.

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c = 1, which is a precursor of the two-dimensional Laughlin state at nu = 1/2. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

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.

Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux

We perform a density-matrix renormalization-group study of strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux. Focusing on one-third filling, we explore the phase diagram in dependence of the magnetic flux and the inter-leg tunneling strength. We find several phases including a Meissner phase, vortex liquids, a vortex lattice, as well as a staggered-current (SC) phase. Moreover, there are regions where the chiral current reverses its direction, both in the Meissner and in the SC phase. While the reversal in the latter case can be ascribed to spontaneous breaking of translational invariance, in the first it stems from an effective flux increase in the rung direction. Interactions are a necessary ingredient to realize either type of chiral-current reversal.