Séminaire de probabilités et physique statistique de l'IHES

A Hierarchical Supersymmetric Model for Weakly Disordered 3d Semimetals

by Prof. Giovanni Antinucci (University of Zurich)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

An important conjecture in quantum mechanics is that non-interacting, disordered 3d quantum systems should 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 weak disorder. In this talk I will present results for a hierarchical supersymmetric model for a class of 3d quantum systems, called Weyl semimetals. We use rigorous renormalization group methods to compute the correlation functions of the system. In particular, I will report a result about the algebraic decay of the averaged two-point correlation function, compatible with delocalization. Our method is based on a rigorous implementation of RG, reminiscent of the Gawedzki-Kupiainen block spin transformations; the main technical novelty is the multiscale analysis of Gaussian measures with purely imaginary covariances.

Joint work with Luca Fresta and Marcello Porta.

Organized by

Hugo Duminil-Copin