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The Adiabatic Theorem for Many-Body Quantum Systems

Mathematical Physics & Probability

Speaker: Martin Fraas, KU Leuven
Location: 1147 MSB
Start time: Wed, Mar 1 2017, 4:10PM

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 annealing and in studies of topological properties of matter. In this setup, the rate of variation ε 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 derived a version of the adiabatic theorem for gapped ground states of quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo linear response formula for a broad class of gapped interacting systems. The talk is based on a joint work with S. Bachmann and W. De Roeck, https://arxiv.org/abs/1612.01505.