数理物理セミナー: Hall-conductivity in periodic infinite-volume Systems (Marius Wesle 氏)

Time： 17:00-18:00

Place：理学部3号館 3-210

Speaker：Marius Wesle 氏 (Tuebingen university)

Title：Hall-conductivity in periodic infinite-volume Systems

Abstract：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.