分野別セミナー

アブストラクト：Given a 2-dimensional system of interacting electrons, one can apply an electric field of strength ε in one coordinate direction and consider the current that this induces in the perpendicular direction. One then
defines the Hall conductivity to be the linear coefficient in the asymptotic expansion of this current response with
respect to ε. In this talk I will explain how in infinitely extended periodic systems of interacting lattice fermions, one can rigorously realise the linear response definition of the Hall-conductivity described above using the NEASS (Non-Equilibrium Almost Stationary State) approach to linear response theory. In the process we will recover a many-body version of the double-commutator formula, which is a well known formula for the Hall-conductivity in non-
interacting systems, and show that the current response is purely linear with no polynomial corrections. Our proof
also allows for a simple argument that shows that the Hall-conductivity is constant within symmetry protected
topological phases.