Time-dependent properties of one-dimensional spin-systems : a DMRG-study
type: CreativeWork
description: In this thesis we have applied the DMRG method to calculate dynamical and time-dependent properties of one-dimensional spin systems. Two different kinds of DMRG algorithms have been applied, and improved or generalized. In the correction vector DMRG used to calculate dynamical structure factors, the most time-consuming step is to solve a system of complex linear equations A|x>=|b> with A and |b> given where the matrix A is non-hermitian. In this work we have used the so-called "GMRES"-algorithm so solve for real and imaginary part of |x> simultaneously. Since this avoids squaring the matrix it leads to a speed-up of the algorithm. We have applied this improved correction vector DMRG to a spin-$1$ Heisenberg chain in a strong external magnetic field. The results of this study are summarized below. The second kind of DMRG algorithm that has been used in this thesis is the recently developed adaptive time-dependent DMRG (adaptive t-DMRG). It allows us to calculate the time-evolution of a given quantum many-body state under the action of a certain time-independent system hamiltonian. In its original formulation the adaptive t-DMRG is restricted to hamiltonians containg only short range interactions because the time-evolution operator has to be split up into local operators via a Suzuki-Trotter decomposition. In this work we have implemented a generalization of this algorithm to hamiltonians containing arbitrary interactions basd on ideas by Steven R. White. Several different time-evolution algorithms and sets of target states have been used and compared. The optimal choice among the algorithms tested is a Krylov subspace algorithm allowing for extremely long time steps and hence leading to short calculation times. In this form the adaptive t-DMRG shows at least comparable performance on systems where also Suzukmi-Trotter algorithms could be used. We have used the adaptive t-DMRG to calculate the time-evolution of a single electronic spin in a semiconductor quantum dot d…
abstract: In this thesis we have applied the DMRG method to calculate dynamical and time-dependent properties of one-dimensional spin systems. Two different kinds of DMRG algorithms have been applied, and improved or generalized. In the correction vector DMRG used to calculate dynamical structure factors, the most time-consuming step is to solve a system of complex linear equations A|x>=|b> with A and |b> given where the matrix A is non-hermitian. In this work we have used the so-called "GMRES"-algorithm so solve for real and imaginary part of |x> simultaneously. Since this avoids squaring the matrix it leads to a speed-up of the algorithm. We have applied this improved correction vector DMRG to a spin-$1$ Heisenberg chain in a strong external magnetic field. The results of this study are summarized below. The second kind of DMRG algorithm that has been used in this thesis is the recently developed adaptive time-dependent DMRG (adaptive t-DMRG). It allows us to calculate the time-evolution of a given quantum many-body state under the action of a certain time-independent system hamiltonian. In its original formulation the adaptive t-DMRG is restricted to hamiltonians containg only short range interactions because the time-evolution operator has to be split up into local operators via a Suzuki-Trotter decomposition. In this work we have implemented a generalization of this algorithm to hamiltonians containing arbitrary interactions basd on ideas by Steven R. White. Several different time-evolution algorithms and sets of target states have been used and compared. The optimal choice among the algorithms tested is a Krylov subspace algorithm allowing for extremely long time steps and hence leading to short calculation times. In this form the adaptive t-DMRG shows at least comparable performance on systems where also Suzukmi-Trotter algorithms could be used. We have used the adaptive t-DMRG to calculate the time-evolution of a single electronic spin in a semiconductor quantum dot d…
author: Friedrich, Andreas
language: eng
keywords: info:eu-repo/classification/ddc/530, Physik
date published: 2006
date modified: 2026-07-30T19:43:10Z
provider: RWTH Aachen University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Publikationsserver der RWTH Aachen University