Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

摘要

In the presence of randomness, a relativistic semimetal undergoes a quantumtransition towards a diffusive phase. A standard approach relates thistransition to the $U(N)$ Gross-Neveu model in the limit of $N o 0$, whilerare events were argued to be relevant close to the transition. In this work wereconcile previous studies by developing a functional renormalization groupamenable to include non-perturbative effects. We show that the previouslyconsidered fixed point is indeed infinitely unstable, confirming the necessityto describe fluctuations beyond the Gaussian approximation. Furthermore, thedisorder distribution renormalizes following the so-called porous mediumequation. We find that the transition is controlled by a non-analytic fixedpoint drastically different from the fixed point of the $U(N)$ Gross-Neveumodel. We relate a self-similar solution of the porous medium equation to amechanism of generation of a finite density of states at the nodal pointresponsible for the transition.