Abstract
We review two rigorous results on the transport properties of weakly interacting fermionic systems on 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.
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