A supersymmetric hierarchical model for weakly disordered $3d$ semimetals

Abstract

In this paper we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

“…The analysis carried out in this paper is inspired by [6], where SUSY and renormalization group have been used to study a massless hierarchical model for disordered three-dimensional semimetals. One of the main obstacles in the control of SUSY integrals for disordered systems is represented by the presence of mostly complex reference Gaussian "measures".…”

Anomaly non-renormalization in interacting Weyl semimetals

“…[21,22]. Interaction [23][24][25][26][27][28][29][30][31][32] and disorder [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] effects in Weyl semimetals have been previously considered, but the issue of the anomaly non-renormalization has not been addressed yet.…”