Quantum effects in one-dimensional optical flat-band lattices

Abstract

I numerically simulated one-dimensional lattice systems describable by the Hubbard-model and containing a flat-band. I studied the manner in which particles initially held in place by a parabolic confinement potential are dispersed across the lattice after the potential is removed. I also studied currents flowing within one-dimensional Hubbard-rings. In both of these cases I observed that the flat dispersion relation of the flat-band manifests itself as the immobility of the particles occupying it. Particles occupying flat-band states do not disperse even after the removal of any external confinement, neither do they contribute to a current within a ring.