Universality of charge transport in weakly interacting fermionic systems

TL;DR

This paper reviews rigorous results demonstrating the universality of charge transport properties, such as conductivity, in weakly interacting fermionic systems on 2D lattices, including graphene and quantum Hall systems.

Contribution

It establishes the universality and stability of charge transport phenomena in weakly interacting fermionic systems using advanced mathematical techniques.

Findings

Universality of longitudinal conductivity in interacting graphene.

Universality of transverse conductivity in gapped fermionic systems.

Stability of the integer quantum Hall effect against weak interactions.

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.