Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders

Abstract

We numerically investigate the expansion of clouds of hard-core bosons in the two-dimensional square lattice using a matrix-product-state--based method. This nonequilibrium setup is induced by quenching the trapping potential to zero and our work is specifically motivated by a recent experiment with interacting bosons in an optical lattice [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)]. As the anisotropy of the amplitudes ${J}_{x}$ and ${J}_{y}$ for hopping in different spatial directions is varied from the one- to the two-dimensional case, we observe a crossover from a fast ballistic expansion in the one-dimensional limit ${J}_{x}\ensuremath{\gg}{J}_{y}$ to much slower dynamics in the isotropic two-dimensional limit ${J}_{x}={J}_{y}$. We further study the dynamics on multileg ladders and long cylinders. For these geometries we compare the expansion of a cloud to the melting of a domain wall, which helps us to identify several different regimes of the expansion as a function of time. By studying the dependence of expansion velocities on both the anisotropy ${J}_{y}/{J}_{x}$ and the number of legs, we observe that the expansion on two-leg ladders, while similar to the two-dimensional case, is slower than on wider ladders. We provide a qualitative explanation for this observation based on an analysis of the rung spectrum.