nils/C> ./gen_matrix4ED -h ********************************************************** gen_matrix4ED: prints matrix for 1D Heisenberg model Version: 0.4, 25.06.2007 by Nils Bluemer options: -N# number of spins -m# mz sector (0<=m<=N) -o open boundary conditions -F ferromagnetic model -v# adjust verbosity (default: 1) -h this help nils/C> ./gen_matrix4ED -N4 -m4 # Hamiltonian for 4 spin AF Heisenberg model (mz=4) 1 4 nils/C> ./gen_matrix4ED -N4 -m2 # Hamiltonian for 4 spin AF Heisenberg model (mz=2) 4 0 2 0 2 2 0 2 0 0 2 0 2 2 0 2 0 nils/C> ./gen_matrix4ED -N4 -m2 | ./ED_jacobi -v0 Eigen values: 4.00000 0.00000 0.00000 -4.00000 nils/C> ./gen_matrix4ED -N4 -m2 | ./ED_jacobi -v1 Original matrix A: 0.00000 2.00000 0.00000 2.00000 2.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 2.00000 0.00000 2.00000 0.00000 Eigenvalues: Eigen values: 4.00000 0.00000 0.00000 -4.00000 final Eigenvectors: 0.50000 0.27156 -0.65288 0.50000 0.50000 -0.65288 -0.27156 -0.50000 0.50000 -0.27156 0.65288 0.50000 0.50000 0.65288 0.27156 -0.50000 nils/C> ./gen_matrix4ED -N4 -m0 | ./ED_jacobi -v1 Original matrix A: 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 -4.00000 2.00000 2.00000 0.00000 2.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 0.00000 2.00000 2.00000 -4.00000 2.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 Eigenvalues: Eigen values: 4.00000 0.00000 0.00000 -0.00000 -4.00000 -8.00000 final Eigenvectors: 0.40825 -0.47689 -0.72280 -0.01140 0.00000 -0.28868 0.40825 -0.00000 -0.00000 0.00000 -0.70711 0.57735 0.40825 0.79857 -0.18540 0.27914 0.00000 -0.28868 0.40825 0.04304 0.33009 -0.79949 -0.00000 -0.28868 0.40825 0.00000 0.00000 -0.00000 0.70711 0.57735 0.40825 -0.36471 0.57812 0.53175 -0.00000 -0.28868 nils/C> ./gen_matrix4ED -N4 -m0 | ./ED_jacobi -v2 Original matrix A: 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 -4.00000 2.00000 2.00000 0.00000 2.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 2.00000 0.00000 2.00000 2.00000 -4.00000 2.00000 0.00000 2.00000 0.00000 0.00000 2.00000 0.00000 Eigenvalues: Matrix A after 1 Jacobi sweeps (12 rotations): 3.54345 1.44866 0.51934 0.58043 -0.69876 0.39059 1.44866 -7.81253 0.19033 0.23241 -0.05401 -0.00124 0.51934 0.19033 0.07383 0.08241 -0.00654 0.05512 0.58043 0.23241 0.08241 0.09194 -0.00142 0.06187 -0.69876 -0.05401 -0.00654 -0.00142 -3.93537 0.00000 0.39059 -0.00124 0.05512 0.06187 0.00000 0.03868 Matrix A after 2 Jacobi sweeps (24 rotations): 3.99986 0.03466 -0.00830 -0.00863 0.00412 -0.00020 0.03466 -7.99990 -0.00074 -0.00091 0.00027 0.00000 -0.00830 -0.00074 0.00002 0.00002 -0.00000 0.00000 -0.00863 -0.00091 0.00002 0.00002 -0.00000 0.00000 0.00412 0.00027 -0.00000 -0.00000 -4.00000 0.00000 -0.00020 0.00000 0.00000 0.00000 0.00000 0.00000 Matrix A after 3 Jacobi sweeps (30 rotations): 4.00000 0.00000 0.00000 0.00000 0.00000 -0.00020 0.00000 -8.00000 -0.00000 0.00000 0.00026 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00001 -0.00000 0.00000 0.00000 -0.00000 -0.00000 0.00001 -0.00000 0.00000 0.00026 0.00001 0.00001 -4.00000 0.00000 -0.00020 0.00000 -0.00000 -0.00000 0.00000 0.00000 Matrix A after 4 Jacobi sweeps (45 rotations): 4.00000 -0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -8.00000 -0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -4.00000 0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 Matrix A after 5 Jacobi sweeps (60 rotations): 4.00000 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 -8.00000 -0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 -4.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 0.00000 Matrix A after 6 Jacobi sweeps (71 rotations): 4.00000 -0.00000 -0.00000 0.00000 -0.00000 0.00000 -0.00000 -8.00000 -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -4.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 Matrix A after 7 Jacobi sweeps (74 rotations): 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -8.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -4.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 Matrix A after 8 Jacobi sweeps (75 rotations): 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -8.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Eigen values: 4.00000 0.00000 0.00000 -0.00000 -4.00000 -8.00000 final Eigenvectors: 0.40825 -0.47689 -0.72280 -0.01140 0.00000 -0.28868 0.40825 -0.00000 -0.00000 0.00000 -0.70711 0.57735 0.40825 0.79857 -0.18540 0.27914 0.00000 -0.28868 0.40825 0.04304 0.33009 -0.79949 -0.00000 -0.28868 0.40825 0.00000 0.00000 -0.00000 0.70711 0.57735 0.40825 -0.36471 0.57812 0.53175 -0.00000 -0.28868