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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Quantum Mechanics

MP 7.1: Hauptvortrag

Dienstag, 14. März 2017, 16:30–17:15, SFG 2010

The Adiabatic Theorem for Many-Body Quantum Systems — Sven Bachmann², Wojciech De Roeck¹, and •Martin Fraas¹ — ¹KU Leuven, Leuven, Belgium — ²LMU, Munich, Germany

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g. in quantum computing, linear response theory for QHE, and in control protocols for artificial states of matter. In this setup, the rate of variation of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. We prove a version of the adiabatic theorem for gapped ground states of quantum spin systems, under assumptions that remain valid in the thermodynamic limit. A direct consequence is a mathematical proof of the Kubo linear response formula for a broad class of interacting systems.