Regensburg 2010 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 30: CE: Low-dimensional Systems - Models 1
TT 30.13: Vortrag
Donnerstag, 25. März 2010, 12:45–13:00, H20
A new approach for the diagonalization of the Hubbard model using basis reordering — •Ralf Gamillscheg1, Gundolf Haase2, and Wolfgang von der Linden1 — 1Institute for Theoretical and Computational Physics, Graz University of Technology, Austria — 2Institute for Mathematics and Scientific Computing, Karl-Franzens-University Graz, Austria
We present a new approach to obtain an effective Hamiltonian for many-particle systems which we call the Two-Subsystem Groundstate Approximation (TSGSA). The method was inspired by the so-called Automated Multilevel Substructuring Method (AMLS). Originally, it relies on subdividing the physical space into several regions. In these sub-systems the eigenproblem is solved, and the regions are combined in an adequate way. We developed a method to partition the state space of a many particle system in order to apply similar operations on the partitions. The tensorial structure of the Hamiltonians of these many-body systems make them even more suitable for this approach.
The method allows to break down the complexity of large many-body systems to the complexity of two spatial sub-systems having half the size. Considering the exponential size of the Hilbert space with respect to the system size this represents a huge advantage.
We will show applications of this method for ground-state calculations and for determining dynamical observables like the single-particle Green's function.