GenericHamiltonianDiagonalization

GenericHamiltonianDiagonalization is a simple program that diagonalizes a matrix (or a sum of matrice) given as an input file.

Binary matrices

The basic usage for an hamiltonian stored as a binary file is

$PATHTODIAGHAM/build/src/Programs/GenericHamiltonianDiagonalization --use-lapack -o spectrum.dat --bin-hamiltonian hamiltonian.mat

where hamiltonian.mat is the matrix binary file and spectrum.dat is the output file for the spectrum. The hamiltonian can be rescaled using the --rescaling-factor option. The diagonal matrix elements can be modified by providing an external column based ASCII text file:

$PATHTODIAGHAM/build/src/Programs/GenericHamiltonianDiagonalization --use-lapack -o spectrum.dat --bin-hamiltonian hamiltonian.mat --rescaling-factor 2.0 --add-diagonal diagonal.dat --column-diagonal 2

In this example, diagonal.dat is the text file containing the contribution that will be added to the diagonal entries of hamiltonian.mat. Note that the rescaling is performed before changing the diagonal entries. The column of diagonal.dat that should be considered is set by --column-diagonal (0 being the first column, the default value of --column-diagonal).

A linear combination of matrices can be used as the input hamiltonian. For example

$PATHTODIAGHAM/build/src/Programs/GenericHamiltonianDiagonalization --use-lapack -o test2 --multiple-binhamiltonians hamiltonians.dat --column-diagonal 3 --add-diagonal diagonal.dat --rescaling-factor 2.0

will first read a list of matrices from the column formatted text file hamiltonians.dat, add them (with the optional weight), rescale by --rescaling-factor and then add diagonal.dat to the diagonal entries. hamiltonians.dat should look like

   hamiltonian1.mat
   hamiltonian2.mat
   hamiltonian3.mat

If the second column is present, it will be used as weights i.e.

   hamiltonian1.mat 0.25
   hamiltonian2.mat 0.75

will correspond to a hamiltonian (hamiltonian1.mat * 0.25) + (hamiltonian2.mat * 0.75).

If the third column is present, it will be used as phases (in unit of <math>2 \pi</math>) to transform the real symmetric matrices in the first column into hermitian matrices. For example:

   hamiltonian1.mat 0.25 0.0
   hamiltonian2.mat 0.75 0.1

will correspond to a hamiltonian (hamiltonian1.mat * 0.25) + (hamiltonian2.mat.herm * 0.75), where hamiltonian2.mat.herm is the matrix formed by multiplying all of the upper triangular elements of hamiltonian2.mat by a factor <math>e^{2 \pi i * 0.1}</math> (and the lower triangular elements by a factor <math>e^{-2 \pi i * 0.1}</math>).

The eigenstates can be obtained using the standard options of DiagHam (such as --eigenstate) except that a prefix for the eigenstate file name should be provided using the --eigenstate-file option.