@phdthesis{Hager2006,
  author    = {Georg Hager},
  title     = {A Parallelized Density Matrix Renormalization Group Algorithm and its Application to Strongly Correlated Systems},
  journal    = {Ein parallelisierter Dichtematrix-Renormierungsgruppen-Algorithmus und seine Anwendung auf stark korrelierte Quantensysteme},
  url       = {https://nbn-resolving.org/urn:nbn:de:gbv:9-000024-1},
  year      = {2006},
  abstract  = {This work studies different alternatives for parallelization of ground-state DMRG, with a focus on shared memory multiprocessor systems. Exploiting the parallelism in the dominant part of a DMRG calculation (diagonalization of the superblock Hamiltonian), speedups of 5 to 6 on 8-CPU machines can be achieved. A performance analysis gives hints as to which machine is best siuted for the task. The parallelized DMRG code is then applied to current problems in theoretical solid state physics with electronics, bosonic and spin degrees of freedom. Stripe-like modulations of the hole density in the ground state of doped Hubbard with cylindrical boundary conditions are idenficied in the thermodynamic limit using extrapolation techniques. In the 1D Holstein model of spinless fermions at half filling, Luttinger parameters and the charge structure factor are determinde in order to derive the phase diagram that had previously been established only on small lattices. For the 1D half-filled Holstein-Hubbard model, a finite size analysisof spine and charge excitation gaps in the relevant sectors (Mott insulator, Peierls band insulator and bipolaronic Peierls insulator) is able to yield the phase diagram as well. Finally, is the Heisenberg spin chain with dynamical phonons is considered as a relevant model for a spin-Peierls transition in Copper Germanate. Using DMRG, the relation between singlet-triplet excitation gap and dynamical dimeriaztion is calculated for the first time.},
  language  = {en}
}