Dresden 2009 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 20: Correlated Electrons: (General) Theory 1

TT 20.3: Vortrag

Dienstag, 24. März 2009, 16:00–16:15, HSZ 301

Upper bound of truncation errors in continuous unitary transformations — •Nils A. Drescher1, Tim Fischer1, and Götz S. Uhrig1,21Technische Universität Dortmund, Lehrstuhl für Theoretische Physik I, 44221 Dortmund, Germany — 2School of Physics, University of New South Wales, Kensington 2052, Sydney NSW, Australia

Self-similar continuous unitary transformations (CUTs) are a method to systematically derive effective models for many-particle-systems of finite or infinite size. They allow us to separate Hilbert spaces of different numbers of quasiparticle. Technically this is done by solving the flow equations for the coefficients of the various terms in the Hamiltonian. In order to keep the number of equations finite truncations are inevitable. The choice of an efficient truncation scheme which preserves the relevant physics is a highly non-trivial task. Here we present the mathematical derivation of a method to quantify the truncation error so that different truncation schemes can be compared without bias. Thereby we can establish rigorous bounds on the accuracy of the ground state energy calculated by CUT. Exemplary results a shown for zero and one dimensional systems[1,2].

[1] S. Dusuel and G.S. Uhrig, Journal of Physics A: Mathematics and General 37, 9275- (2004).

[2] C. Knetter, K.P. Schmidt, and G.S. Uhrig, Journal of Physics A: Mathematics and General 36(29), 7889 (2003).

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