Regensburg 2007 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 20: Correlated Electrons - Poster Session
TT 20.80: Poster
Mittwoch, 28. März 2007, 14:00–17:45, Poster A
Improved scaling for the Matrix Product State alternative to DMRG — •Peter Pippan1, Steven White2, and Hans Gerd Evertz1 — 1Theor. and Comput. Physics, TU Graz, 8010 Graz, Austria — 2Dept of Physics and Astronomy, UC Irvine, CA 92697, USA
The density-matrix renormalization group (DMRG) is a highly efficient algorithm for the investigation of low-dimensional, strongly correlated systems. It converges to the ground state, which can be written as a matrix product state. We study a recently proposed variational method that optimizes these matrix product states independently of DMRG. This method proofs useful for periodic boundary conditions and is conceptually more powerfull than DMRG, but is numerically much less efficient. We introduce a decomposition of large matrices using a singular value decomposition (SVD). Neglecting small singular values, we approximate the matrices very accurately while keeping storage requirements small. The computational effort and especially its scaling with system size is then drastically reduced, while accuracy remains unchanged. This allows the investigation of much larger systems with periodic boundary conditions. Properties of the new method are studied for the Spin 1 Heisenberg chain.