Marcello Porta: Edge transport in interacting quantum Hall systems

Abstract: The bulk-edge correspondence is a remarkable duality in condensed matter physics, relating the value of bulk topological invariants to the emergence of gapless edge modes. In the case of the integer quantum Hall effect, the value of the Hall conductivity is equal to the sum of signed edge modes, taking into account their chirality. For noninteracting systems, this fact is by now understood in full mathematical rigor. For interacting models, in the last years there has been progress in the rigorous understanding of bulk topological phases, but a lot less is known about interacting edge modes and about the bulk-edge duality. From the point of view of effective QFTs, the edge modes of 2d Hall systems are expected to be well described by the multichannel Luttinger model, a 1+1 dimensional integrable QFT. In this talk I will discuss how rigorous RG methods can be used to prove the emergence of the Luttinger liquid description from the 2d lattice model, and to control the deviations away from it at finite scales. The approach allows to exactly compute real-time edge transport coefficients, and in particular to prove the quantization of the edge conductance, thanks to the combination of lattice and emergent Ward identities. Joint work with Vieri Mastropietro.

*Marcello Porta, SISSA Trieste