Quantum Monte Carlo simulation of confined bosonic atoms in optical lattices

We study static properties of ultra-cold bosonic atoms in two-dimensional optical lattices by quantum Monte Carlo simulations of the bosonic Hubbard model in parabolic confinement potentials. Our focus is on local probes identifying Mott-insulating and superfluid regions, which can coexist in the inhomogenous environment of the trap. By proposing an effective ladder model for the boundary region between the two phases we can show clear evidence for the absence of true quantum critical behavior and explain the absence of critical slowing down at the quantum phase transition in a harmonic trap.