Universality of charge transport in weakly interacting fermionic systems

Abstract

We review two rigorous results on the transport properties of weakly interacting fermionic systems on $2d$ lattices, in the linear response regime. First, we discuss the universality of the longitudinal conductivity for interacting graphene. Then, we focus on the transverse conductivity of general weakly interacting gapped fermionic systems, and we establish its universality. This last result proves the stability of the integer quantum Hall effect against weak interactions. The proofs are based on combinations of fermionic cluster expansion techniques, renormalization group and lattice Ward identities.

8 pages, no figures. Contribution to the proceedings of the XVIII International Congress on Mathematical Physics, Santiago de Chile, July 27 - August 1, 2015

References in corpus (6)

• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• The optical conductivity of graphene in the visible region of the spectrum
• Coulomb interaction, ripples, and the minimal conductivity of graphene
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