Mathematical Physics and Harmonic Analysis Seminar

Date: October 7, 2022

Time: 1:50PM - 2:50PM

Location: BLOC 306

Speaker: Rodrigo Matos , TAMU

Title: Eigenvalue statistics for the disordered Hubbard model within Hartree-Fock theory

Abstract: Localization in the disordered Hubbard model within Hartree-Fock theory was previously established in joint work with J. Schenker, in the regime of large disorder in arbitrary dimension and at any disorder strength in dimension one, provided the interaction strength is sufficiently small. I will present recent progress on the spectral statistics conjecture for this model. Under weak interactions and for energies in the localization regime which are also Lebesgue points of the density of states, it is shown that a suitable local eigenvalue process converges in distribution to a Poisson process with intensity given by the density of states times Lebesgue measure. If time allows, proof ideas and further research directions will be discussed, including a Minami estimate and its applications.