Heidelberg 2015 – wissenschaftliches Programm
Q 18.2: Vortrag
Dienstag, 24. März 2015, 11:15–11:30, K/HS1
Local constants of motion imply transport — Mathis Friesdorf1, •Marcel Goihl1, Albert H. Werner1, Winton Brown2, and Jens Eisert1 — 1Dahlem Center for Complex Quantum Systems, Freie Universitaet Berlin, 14195 Berlin, Germany — 2Computer Science Department, University College London, London WC1E 6BT
Generic interacting many-body systems are usually expected to thermalise following out of equilibrium dynamics: Local expectation values should be captured in terms of thermal ensembles. This behaviour necessarily relies on transport in the system, in the sense that information spreads outside of any finite region. A notable class of models that contradicts this intuition is given by systems exhibiting many-body localisation. Their eigenstates are strongly lacking entanglement, concomitant with an absence of thermalisation. The description of these models often relies on local constants of motion, certain operators that remain local even for infinite times. In this work, we show that counter-intuitively, the existence of such operators, together with a suitable non-degenerate Hamiltonian spectrum, implies that there exist other operators for which the system has to have transport. While upper bounds on transport have long been known, lower bounds have only been obtained for very specific models. Our results constitute an important step towards proving transport in generic systems.