2020
DOI: 10.1103/physrevresearch.2.023303
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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)-dimensional 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 universa… Show more

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Cited by 5 publications
(2 citation statements)
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References 84 publications
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“…Furthermore, our mean field arguments do not depend on the detailed choice of density-density interaction potential, V int (ρ e ), for the Dirac electrons, which simply maps to a fluxflux interaction, V int (b * ), in the dual theory. In particular, we note that instantaneous Coulomb interactions are expected to be marginally irrelevant at the QED 3 fixed point [64], while a Lorentz invariant generalization of Coulomb interactions is exactly marginal and leads to a line of fixed points with selfdual properties [51,53,65,66].…”
Section: Introductionmentioning
confidence: 92%
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“…Furthermore, our mean field arguments do not depend on the detailed choice of density-density interaction potential, V int (ρ e ), for the Dirac electrons, which simply maps to a fluxflux interaction, V int (b * ), in the dual theory. In particular, we note that instantaneous Coulomb interactions are expected to be marginally irrelevant at the QED 3 fixed point [64], while a Lorentz invariant generalization of Coulomb interactions is exactly marginal and leads to a line of fixed points with selfdual properties [51,53,65,66].…”
Section: Introductionmentioning
confidence: 92%
“…We finally comment that truly realistic systems have quenched disorder, which will cause QED 3 theories to run to a new fixed point governed by an interplay of disorder and interactions [64,[72][73][74][75]. In the N f = 3 theory, PHsymmetric disorder (a random magnetic field component for the electrons) is exactly marginal, leading to a line of fixed points with varying dynamical critical exponent, z > 1.…”
Section: Introductionmentioning
confidence: 97%