Hamburg 2016 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantenmechanik und Quanteninformation

MP 3.1: Invited Talk

Tuesday, March 1, 2016, 16:45–17:30, VMP6 HS B

Towards a unifying view on many-body localisation — •Jens Eisert — Freie Universität Berlin

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. Yet, many aspects of it are still unsatisfactorily understood, a statement that is surely fair from the perspective of mathematical physics.

In this talk, I will make the attempt to bring together several aspects of the phenomenology of many-body localisation, attaining new insights into the mathematical connections between seemingly unrelated features. Ideas of entanglement area laws, Lieb-Robinson bounds, filter functions, approximately local constants of motion, transport, and tensor networks will feature strongly. We will finally hint at how these ideas can be used to detect many-body localisation in the laboratory, discriminating it from Anderson localisation.

[1] Quantum many-body systems out of equilibrium, Nature Physics 11, 124 (2015)

[2] Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys., in press (2016)

[3] Many-body localisation implies that eigenvectors are matrix-product states, Phys. Rev. Lett. 114, 170505 (2015)

[4] Local constants of motion imply information propagation, New J. Phys. 17, 113054 (2015)

[5] Absence of thermalisation in non-integrable systems, Phys. Rev. Lett. 106, 040401 (2011)

[6] Total correlations of the diagonal ensemble herald the many-body localisation transition, Phys. Rev. B 92, 180202(R) (2015)

[7] Experimentally accessible witnesses of many-body localisation, arXiv:1601.02666 (2016)