Scaling and Diffusion of Dirac Composite Fermions

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.

28 + 26 pages; v2: typos corrected

References in corpus (12)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Critical exponent for the quantum Hall transition
• Duality between $(2+1)d$ Quantum Critical Points
• Particle-hole symmetry and the dirty boson problem
• Quantum critical behavior of the superfluid-Mott glass transition
• Quantum Critical Scaling of Dirty Bosons in Two Dimensions
• Quantum-Hall to Insulator Transition in Ultra-low-carrier-density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level
• Self-Dual $\nu =1$ Bosonic Quantum Hall State in Mixed Dimensional QED
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$

Cited by in corpus (3)

• Quantum phase transitions in Dirac fermion systems
• Interaction-induced metallicity in a two-dimensional disordered non-Fermi liquid
• Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction