Using the fractional moment method it is shown that, within the Hartree–Fock approximation for the disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential decay of eigenfunction correlators. Our result holds in any dimension in the regime of large disorder and at any disorder in the one dimensional case. As a consequence of our methods, we are able to show Hölder continuity of the integrated density of states with respect to energy, disorder and interaction.
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We thank the anonymous referee for a number of suggestions and remarks which greatly improved the exposition, in particular the proof of Lemma 11. This work was supported by the National Science Foundation under grants no 1900015 and 2000345.
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Matos, R., Schenker, J. Localization and IDS Regularity in the Disordered Hubbard Model within Hartree–Fock Theory. Commun. Math. Phys. (2021). https://doi.org/10.1007/s00220-020-03933-8