Dresden 2011 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

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.
S. White, Phys. Rev. Lett. 69, 2863 (1992).
S. Östlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995).