Scaling and Diffusion of Dirac Composite Fermions

TL;DR

This paper investigates how quenched disorder and Coulomb interactions influence the quantum phase transitions of an anyon gas modeled by Dirac fermions coupled to a Chern-Simons gauge field, revealing stable fixed points and disorder effects.

Contribution

It provides a large N_f renormalization group analysis of Dirac composite fermions with Coulomb interactions and disorder, identifying stable fixed points and their properties.

Findings

Coulomb interaction is irrelevant at the clean fixed point.

Stable fixed points exist with finite or infinite Coulomb coupling.

Disorder effects depend on the value of θ and symmetry considerations.

Abstract

We study the effects of quenched disorder and a dissipative Coulomb interaction on an anyon gas in a periodic potential undergoing a quantum phase transition. We use a $(2+1)$d low-energy effective description that involves $N_f = 1$ Dirac fermion coupled to a $U(1)$ Chern-Simons gauge field at level $(\theta - 1/2)$. When $\theta = 1/2$ the anyons are free Dirac fermions that exhibit an integer quantum Hall transition; when $\theta = 1$ the anyons are bosons undergoing a superconductor-insulator transition in the universality class of the 3d XY model. Using the large $N_f$ approximation we perform a renormalization group analysis. The dissipative Coulomb interaction allows for two classes of IR stable fixed points: those with a finite, nonzero Coulomb coupling and dynamical critical exponent $z = 1$ and those with an effectively infinite Coulomb coupling and $1 < z < 2$. We find the Coulomb interaction to be an irrelevant perturbation of the clean fixed point for any $\theta$. At $\theta = 1/2$ the clean fixed point is stable to charge-conjugation preserving (random mass) disorder, while a line of diffusive fixed points obtains when the product of charge-conjugation and time-reversal symmetries is preserved. At $\theta = 1$ we find a finite disorder fixed point with unbroken charge-conjugation symmetry whether or not the Coulomb interaction is present. Other cases result in runaway flows. We comment on the relation of our results to other theoretical studies and the relevancy to experiment.