Scaling and Diffusion of Dirac Composite Fermions

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 (θ−1/2). When θ=1/2 the anyons are free Dirac fermions that exhibit an integer quantum Hall transition; when θ=1 the anyons are bosons undergoing a superconductor-insulator transition in the universality class of the 3d XY model. Using the large Nf 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

Keywords:

• Composite fermion
• Quantum phase transition
• Dirac fermion
• Topological quantum computer
• Mathematical physics
• Renormalization group
• Anyon
• Coulomb
• Critical exponent
• Physics

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