Superfluid-to-Mott transition in optical lattices with restricted geometry

We study the influence of the restricted geometry of a cubic lattice confined within a finite slab of L layers (i.e. of the form infinity x infinity x L) on the ground-state properties of interacting bosons in the optical lattice. Using the quantum rotor approach for the Bose-Hubbard model, we quantify how the restricted slab geometry affects the superfluid-to-Mott-insulator transition. For increasing values of L, both the analytical approach for large L and the direct calculation using lattice density of states for any arbitrary L show that the behavior of the system becomes indistinguishable from the cubic bulk case (L = infinity) even for relatively small values of L (L approximate to 10). This may be an important justification for treating bosons in optical lattices using methods of statistical physics pertinent for infinite systems.