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

## TL;DR

This paper develops a rigorous supersymmetric hierarchical model for weakly disordered 3D semimetals, demonstrating algebraic decay of correlations indicative of delocalization, using advanced renormalization group techniques.

## Contribution

It introduces a novel hierarchical supersymmetric model for 3D semimetals and applies rigorous renormalization group methods to analyze their correlation functions.

## Key findings

- Proves algebraic decay of two-point correlations
- Demonstrates delocalization in weakly disordered 3D semimetals
- Develops multiscale analysis for complex Gaussian integrations

## 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.