Mobility edge of the two dimensional Bose-Hubbard model

Understand

We analyze the disorder driven localization of the two dimensional Bose-Hubbard model by evaluating the full low energy quasiparticle spectrum via a recently developed fluctuation operator expansion method.

• For any strength of the local interaction we find a mobility edge that displays an approximately exponential decay with increasing disorder strength.
• We determine the finite-size scaling collapse and exponents at this critical line finding that the localization of excitations is characterized by weak multi-fractality and a thermal-like critical gap ratio.
• A direct comparison to a recent experiment yields an excellent match of the predicted finite-size transition point and scaling of single particle correlations.