Mobility edge of the two dimensional Bose-Hubbard model

26 Jun 2020  ·  Geißler Andreas, Pupillo Guido ·

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. For any strength of the local interaction we find a mobility edge that displays an approximately exponential decay with disorder... 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. read more

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Quantum Gases Disordered Systems and Neural Networks Quantum Physics