The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with
results from exactly solvable models and computational approaches, the concept of bosonic …

During the last decade, many exciting phenomena have been experimentally observed and
theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid …

We use the density-matrix renormalization group method to investigate ground-state and
dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of …

We use strong-coupling perturbation theory, the variational cluster approach (VCA), and the
dynamical density-matrix renormalization group (DDMRG) method to investigate static and …

Recent experiments in ultracold atoms and photonic analogs have reported the
implementation of artificial gauge fields in lattice systems, facilitating the realization of …

We report on the investigation of the three-dimensional single-atom-resolved distributions of
bosonic Mott insulators in momentum space. First, we measure the two-body and three-body …

We carry out a perturbative analysis, of high order in the tunneling parameter, of the ground
state of the homogeneous Bose-Hubbard model in the Mott insulator phase. This is made …

We study the phase diagram and nonequilibrium dynamics involving ramp of the hopping
amplitude J (t)= J t/τ with ramp time τ of the Bose-Hubbard model at zero temperature using …

We present a nonperturbative renormalization-group approach to the Bose-Hubbard model.
By taking as initial condition of the renormalization-group flow the (local) limit of decoupled …

We study the Bose-Hubbard and Fermi-Hubbard models in the (formal) limit of large
coordination numbers Z≫ 1. Via an expansion into powers of 1/Z, we establish a hierarchy …