Universal edge currents in interacting quantum Hall systems

Vortrag von Prof. Dr. Marcello Porta

Datum: 03.05.18  Zeit: 18.10 - 19.00  Raum: Y27H35/36

Two-dimensional quantum systems display remarkable transport properties. The paradigmatic example is the integer quantum Hall effect: the bulk transverse conductivity of gapped quantum systems exposed to strong magnetic fields only takes quantized values. A dual aspect of the quantization of bulk transport is the emergence of gapless edge modes, carrying dissipationless edge currents. This phenomenon is called the bulk-edge correspondence. The last decade witnessed important mathematical progress in the understanding of the quantization of the bulk Hall conductivity for many-body quantum systems. In contrast, much less is known about the bulk-edge duality, beyond the single-particle approximation. In this talk, I will present a theorem establishing the bulk-edge correspondence for a class of two-dimensional many-body quantum systems, displaying single-mode edge currents. More generally, our result provides the first rigorous justification of the celebrated chiral Luttinger liquid theory of quantum Hall edge states. Joint work with G. Antinucci and V. Mastropietro.