Regensburg 2019 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Dynamics in many-body systems: Equilibration and localization I (joint session DY/TT)
DY 6.2: Vortrag
Montag, 1. April 2019, 10:15–10:30, H19
Entanglement-ergodic quantum systems equilibrate exponentially well — Henrik Wilming1, •Marcel Goihl2, Ingo Roth2, and Jens Eisert2 — 1Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland — 2Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results have been proven that show that equilibration is generic provided that the initial state has overlap with sufficiently many energy levels and the energy spectrum is sufficiently generic. At the same time results showing that natural initial states fulfill this condition are lacking. We present stringent results for equilibration of lattice systems in which the amount of entanglement in energy eigenstates with finite energy density is extensive for some subset of the lattice. Concretely, we carefully formalize a notion of "entanglement-ergodicity" in terms of Rényi entropies and derive that systems fulfilling this condition equilibrate exponentially well. Our proof uses insights about Rényi entropies and combines them with recent results about the probability distribution of energy in local lattice systems with initial states that are weakly correlated.