Quantum 2025 – wissenschaftliches Programm
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TUE: Tuesday Contributed Sessions
TUE 10: Foundational / Mathematical Aspects – Rigorous Results
TUE 10.6: Vortrag
Dienstag, 9. September 2025, 15:30–15:45, ZHG103
Macroscopic Hall-Current Response in Infinite-Volume Systems — •Marius Wesle1, Giovanna Marcelli2, Tadahiro Miyao3, Domenico Monaco4, and Stefan Teufel1 — 1Universität Tübingen, Germany — 2Università di Roma Tre, Italy — 3Hokkaido University, Japan — 4Sapienza Università di Roma, Italy
Given a 2-dimensional system of interacting fermions, the Hall-conductivity is defined as the linear response coefficient that is associated to the current induced in one direction when applying a homogeneous electric field in the perpendicular direction.
In this talk I will explain how in infinitely-extended periodic systems of interacting lattice fermions with a spectral gap, one can rigorously realise the linear response definition of the Hall-conductivity described above. By using the NEASS (Non-Equilibrium Almost-Stationary State) approach to linear response theory we can rigorously control the induced Hall-current, despite the fact that even a very small homogeneous electric field closes the spectral gap. Our proof recovers a many-body version of the double-commutator formula for the Hall-conductivity and shows, that the current response is purely linear with no polynomial corrections. It also allows for a simple argument that shows that the Hall-conductivity is constant within topological phases. This talk is based on arXiv:2411.06967.
Keywords: Quantum Hall Effect; Linear Response; Infinite Volume; Topological Phases; Kubo Formula