Self-Consistent Approach for Mapping Interacting Systems in Continuous Space to Lattice Models

We propose a general variational principle for mapping the interacting systems in continuous space to lattice models. Based on the principle, we derive a set of self-consistent nonlinear equations for the Wannier functions (or, equivalently for the Bloch functions). These equations show that the Wannier functions can be strongly influenced by the interaction and be significantly different from their non-interacting counterparts. The approach is demonstrated with interacting bosons in an optical lattice, and illustrated quantitatively by a simple model of interacting bosons in a double well potential. It is shown that the so-determined lattice model parameters can be significantly different from their non-interacting values.