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TT: Fachverband Tiefe Temperaturen

TT 44: Poster Session Correlated Electrons

TT 44.88: Poster

Thursday, March 17, 2011, 10:00–13:00, P1

Compression of matrix-product states — •Michael Lee and Michael Potthoff — I. Institut für Theoretische Physik, Jungiusstraße 9, 20355 Hamburg

One-dimensional systems of strongly correlated electrons can efficiently be treated by means of the density-matrix renormalization group (DMRG) [1]. It has been shown [2] that an essentially equivalent formulation of the DMRG is possible using matrix-product states and matrix-product operators.

We propose to employ Krylov-based techniques operating on the space of matrix-product states. This should allow for a calculation of dynamical correlation functions, like the one-particle Green’s function, similar to a standard Lanczos calculation without the need for multiple-state targeting. Unlike the correction-vector method this “matrix-product-Lanczos approach” offers the exciting perspective to get the entire frequency dependence of the Green’s function from a single calculation.

The iterative algorithm requires a “compression” of matrix-product states of the form H|Ψ⟩ to control the growth of matrix dimensions. Here, we show first results and discuss the accuracy and efficiency of the compression technique.
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