Finite size effects for interacting bosons on small ring lattices

Abstract We study the stationary properties of interacting ultracold bosons in a small one dimensional ring-shaped lattices within a Bose–Hubbard model using finite density matrix renormalization group. Small system size highlights the impact of the periodic boundary condition on the phase transition boundaries and the density–density correlation. Heat maps, as a function of chemical potential and hopping coupling, of differential expectations with respect to the ground and the excited states of energy, entropy and particle number, display a oscillatory stripe pattern that follow the trend of the phase boundaries. These features progressively diminish with system size, and are qualitatively independent of the boundary condition. A mean field analysis demonstrates that the striping is a finite size effect. The momentum distribution as a function of a phase on the hopping potential displays flux quantization effects of the non-trivial topology.