Dresden 2011 – wissenschaftliches Programm

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MA: Fachverband Magnetismus

MA 45: Micromagnetism/ Computational Magnetics

MA 45.6: Vortrag

Mittwoch, 16. März 2011, 18:45–19:00, HSZ 403

Dynamical simulation of integrable and non-integrable models in the Heisenberg picture — •Dominik Muth, Razmik Unanyan, and Michael Fleischhauer — Fachbereich Physik und Forschungszentrum OPTIMAS, Technische Universität Kaiserslautern, D-67663 Kaiserslautern

The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown, however, that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient as the corresponding operator-space entanglement grows only logarithmically. Using the spin-1/2 XX chain as generic example of an integrabel model that can be mapped to free particles, we here provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature auto correlation function which decays slower than exponential, i.e., with a power law. This is amongst others the case for models where the Blombergen-De Gennes conjecture of high-temperature diffusive dynamics holds. Thus efficient simulability may already be implied by a single conservation law (like that of total magnetization), as we will illustrate numerically for the spin-1 XXZ model. Finally we discuss the advantage of incorporating the conservation law into the algorithm, which can be essential for applications and is frequently implemented in the Schrödinger picture.

Dominik Muth, Razmik G. Unanyann, and Michael Fleischhauer, arXiv:1009.4646