Séminaire de Physique Théorique

Geometry of Quantum Hall states

by Prof. Semyon KLEVTSOV (Université de Cologne)

Amhithéâtre Léon Motchane (IHES)

Amhithéâtre Léon Motchane


IHES Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
I will talk about recent progress in understanding quantum Hall states on curved backgrounds and in inhomogeneous magnetic fields and their large N limits, N being the number of particles. The large N limit of the free energy of the Laughlin states in the integer Quantum Hall is controlled by the Bergman kernel expansion, and, in a sense, is exactly solvable to all orders in 1/N. For the fractional Laughlin states, the large N limit can be determined from free field representation. The terms in the large N expansion are given by various geometric functionals. In particular, the Liouville action shows up at the order O(1) in the expansion, and signifies the effect gravitational anomaly. The appearance of this term leads us to argue for the existence of a third quantized kinetic coefficient, precise on the Hall plateaus, in addition to Hall conductance and anomalous viscosity. Based on: 1309.7333, 1410.6802, 1504.07198 and upcoming work.