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arXiv · 1612.01505

Adiabatic Theorem for Quantum Spin Systems

Sven Bachmann·Wojciech De Roeck·Martin Fraas
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Abstract

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 $\varepsilon$ 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. In this letter, 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. As an application, we give a mathematical proof of Kubo linear response formula for a broad class of gapped interacting systems.

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Sven Bachmann, Wojciech De Roeck, Martin Fraas. 2017-09-27. Adiabatic Theorem for Quantum Spin Systems. https://doi.org/10.1103/physrevlett.119.060201

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