Onset of superfluidity in 2D optical lattices with bond percolation

Here we focus on the effect of hopping disorder on the onset of superfluidity of a BEC immersed in a deep and disordered optical lattice, where the use of the Bose-Hubbard Hamiltonian is justified. We introduce disorder via a bond percolation model by weakening each nearest-neighbor tunneling element with a probability p. We formulate and solve a renormalization-group equation to find the critical percolation threshold Pc and the accompanying critical exponent v. We also analyze a mean field version of the same problem, and an exact ID model and indicate possible experiments that may support our results