Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation

TL;DR

This paper investigates the quantum phase transition in disordered relativistic semimetals, revealing a nonanalytic fixed point through a novel functional renormalization group approach involving the porous medium equation.

Contribution

It introduces a new functional renormalization group method that accounts for non-Gaussian fluctuations and demonstrates the transition is governed by a nonanalytic fixed point, differing from previous models.

Findings

Disorder distribution follows the porous medium equation during renormalization.

The transition is controlled by a nonanalytic fixed point distinct from the Gross-Neveu model.

The approach explains the spontaneous generation of a finite density of states.

Abstract

In the presence of randomness, a relativistic semimetal undergoes a quantum transition towards a diffusive phase. A standard approach relates this transition to the $U(N)$ Gross-Neveu model in the limit of $N \to 0$. We show that the corresponding fixed point is infinitely unstable, demonstrating the necessity to include fluctuations beyond the usual Gaussian approximation. We develop a functional renormalization group method amenable to include these effects and show that the disorder distribution renormalizes following the so-called porous medium equation. We find that the transition is controlled by a nonanalytic fixed point drastically different from that of the $U(N)$ Gross-Neveu model. Our approach provides a unique mechanism of spontaneous generation of a finite density of states and also characterizes the scaling behavior of the broad distribution of fluctuations close to the transition. It can be applied to other problems where nonanalytic effects may play a role, such as the Anderson localization transition.