Negative dimensional operators in the disordered critical points of Dirac fermions

TL;DR

This paper investigates the critical behavior of disordered 2D Dirac fermion systems, revealing a line of critical points with infinitely many relevant operators having negative scaling dimensions, using bosonization and current algebra techniques.

Contribution

It provides an exact analysis of the critical line in disordered Dirac fermion systems, identifying the presence of relevant operators with negative scaling dimensions, which was not previously understood.

Findings

Identified a line of critical points in disordered Dirac fermion systems.

Calculated exact scaling dimensions of local operators.

Discovered an infinite number of relevant operators with negative scaling dimensions.

Abstract

Recently, in an attempt to study disordered criticality in Quantum Hall systems and $d$-wave superconductivity, it was found that two dimensional random Dirac fermion systems contain a line of critical points which is connected to the pure system. We use bosonization and current algebra to study properties of the critical line and calculate the exact scaling dimensions of all local operators. We find that the critical line contains an infinite number of relevant operators with negative scaling dimensions.