Real and Imaginary Part of Conductivity of Strongly Interacting Bosons in Optical Lattices

We calculate the conductivity of strongly interacting bosons described by the Bose-Hubbard model in a twodimensional lattice in controlled gauge potential acting as a uniform external magnetic field. In such scenario, two types of conductivity can be distinguished: intra-and inter-band. The interband contribution, usually omitted in analysis of multiband systems, appears to have a crucial role in the transport properties as its values are a few orders of magnitude greater than the intraband one.