Seminari del Dipartimento
Fisica Matematica A hierarchical supersymmetric model for weakly disordered 3d semimetals Dr. Giovanni Antinucci 12-03-2019 - 14:30 Largo San Leonardo Murialdo, 1 Aula 311
An important open problem in quantum mechanics is to prove that noninteracting, disordered 3d quantum systems exhibit a localization-delocalization transition as a function of the disorder strength. From a mathematical viewpoint, a lot is known about the localized phase for strong disorder, much less about the delocalized phase at small disorder. In this talk I will present results for a hierarchical supersymmetric model for a class of disordered 3d gapless quantum systems, called Weyl semimetals. In the absence of disorder, the main feature of these systems is the pointlike nature of the Fermi surface. We use rigorous renormalization group methods to compute the correlation functions of the system. In particular, I will present a theorem about the algebraic decay of the averaged two-point correlation function, compatible with delocalization. Our method is based on a rigorous implementation of renormalization group, reminiscent of the Gawedzki-Kupiainen block spin transformations; the main technical novelty is the multiscale analysis of massless Gaussian measures with purely imaginary covariances. Joint work with Luca Fresta and Marcello Porta. |