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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 12: Quantenmechanik II

MP 12.1: Talk

Wednesday, March 18, 2015, 16:50–17:10, HFT-FT 101

Lieb-Robinson bounds and Haag-Ruelle scattering theory for gapped quantum spin systems — Sven Bachmann¹, Wojciech Dybalski², and •Pieter Naaijkens³ — ¹Mathematisches Institut der Universität München, Deutschland — ²Zentrum Mathematik, Technische Universität München, Garching, Deutschland — ³Institut für Theoretische Physik, Leibniz Universität Hannover, Deutschland

We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles and the corresponding S-matrix. We discuss the main technical difficulties in translating results from relativistic QFT to lattice systems, and dicusss how Lieb-Robinson bounds can be used to solve these problems.