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Out of equilibrium dynamics and a unifying view on many-body localisation

Presented by: 
Jens Eisert Freie Universität Berlin
Friday 15th January 2016 - 15:00 to 16:00
INI Seminar Room 1
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 - maybe most importantly - in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalisation following out-of-equilibrium dynamics. Still, it seems fair to say that many aspects of it are still unsatisfactorily understood.

In this talk, following an introduction into recent progress on thermalisation of closed quantum systems, I will make the attempt to bring together several aspects of the phenomenology of many-body localisation, attaining new insights into the 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 discuss experimentally accessible witnesses of many-body localisation in cold atomic quantum simulators.

[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 Phys. Rep., in press (2015) [3] Many-body localization 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 thermalization 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 In preparation (2015)
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    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons