Stuttgart 2012 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 35: Poster 2

Q 35.34: Poster

Wednesday, March 14, 2012, 16:30–19:00, Poster.I+II

Bounding Ground State Energies From Below — •Tillmann Baumgratz and Martin B. Plenio — Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany

In contrast to standard variational methods we present a technique that determines lower bounds on the ground state energy of condensed matter systems. This is achieved by relaxing the positivity constraint on the density matrix of the system thus yielding an optimization problem scaling polynomially in the system size. We discuss how symmetries, especially translational invariance, can help to reduce the number of variables in the programme [1]. Further, a novel numerical approach, principally a combination of a projected gradient algorithm with Dykstra’s algorithm, for solving the optimization problem is presented.

[1] T. Baumgratz and M.B. Plenio, arXiv:1106.5275.