# Heidelberg 2015 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 18: Quantum Information: Concepts and Methods III

### Q 18.3: Vortrag

### Dienstag, 24. März 2015, 11:30–11:45, K/HS1

**Many-body localisation implies that eigenvectors are matrix-product states** — •Mathis Friesdorf^{1}, Albert H. Werner^{1}, Winton Brown^{2}, Volkher B. Scholz^{3}, and Jens Eisert^{1} — ^{1}Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany — ^{2}Computer Science Department, University College London, London, England — ^{3}Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland

The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalisation following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties - a vanishing group velocity and the absence of transport - with entanglement properties of individual eigenvectors. Using Lieb-Robinson bounds and filter functions, we prove rigorously under simple assumptions on the spectrum that if a system shows strong dynamical localisation, all of its many- body eigenvectors have clustering correlations. In one dimension this implies directly an entanglement area law, hence the eigenvectors can be approximated by matrix-product states. We also show this statement for parts of the spectrum, allowing for the existence of a mobility edge above which transport is possible.