Emergent space-time supersymmetry at disorder quantum critical point

TL;DR

This paper investigates how different types of weak disorder affect the emergent spacetime supersymmetry at quantum critical points in Dirac and Weyl semimetals, finding that weak disorder does not destabilize the supersymmetry.

Contribution

It provides a systematic renormalization group analysis showing that weak disorder is irrelevant, thus stabilizing emergent supersymmetry in these systems.

Findings

Weak disorder does not destabilize emergent supersymmetry.

The stability holds for various disorder types in (2+1)D Dirac semimetals.

Emergent supersymmetry remains stable under weak disorder in (3+1)D Weyl semimetals.

Abstract

We study the effect of disorder on the spacetime supersymmetry that is proposed to emerge at the quantum critical point of pair density wave transition in (2+1)D Dirac semimetals and (3+1)D Weyl semimetals. In the (2+1)D Dirac semimetal, we consider three types of disorder, including random scalar potential, random vector potential and random mass potential, while the random mass disorder is absent in the (3+1)D Weyl semimetal. Via a systematic renormalization group analysis, we find that any type of weak random disorder is irrelevant due to the couplings between the disorder potential and the Yukawa vertex. The emergent supersymmetry is thus stable for weak random potentials. Our work will pave the way for exploration supersymmetry in realistic condensed matter systems.