Speaker
Prof.
Marcello Porta
Description
In this talk I will discuss the charge transport properties of weakly interacting fermionic
systems, in the zero temperature and infinite volume limit. In the first part of the talk I will consider
general interacting, gapped fermionic systems on periodic two-dimensional lattices. Our theorem states that
the Kubo conductivity matrix is independent of many-body interactions, provided the interaction strength is
small enough. In particular, the result proves the stability of the integer quantum Hall effect against weak
many-body interactions. In the second part of the talk, I will focus on the transitions between different
topological Hall phases in the interacting Haldane model. The Haldane model is a graphene-like model that, in
the absence of interactions, displays a non-trivial topological phase diagram. We consider the model in the
presence of weak many-body interactions, and we give a rigorous construction of the renormalized transition
line. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity
is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and
the longitudinal conductivity do not depend on the interaction. The proofs are based on a combination of
cluster expansion techniques, rigorous renormalization group and Ward identities. Joint work with A.
Giuliani, I. Jauslin and V. Mastropietro.
