Matrix Product Toolkit | Tools / MpAdd

This tool calculates the sum of a list of wavefunctions.

Computational complexity: {$L m^3 d n^2$}, where {$n$} is the number of wavefunctions in the summation. [*]

Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 709:712)
Compiled on Jul 16 2007 at 21:22:41
usage: mp-add [options] -o output-file-name input1 input2 ...
Allowed options:
  --help                    show this help message
  --min-states arg          Minimum number of states to keep [default 1]
  -m [ --max-states ] arg   Maximum number of states to keep [default 100000]
  -r [ --trunc ] arg        Cutoff truncation error per site [default 0]
  -d [ --eigen-cutoff ] arg Cutoff threshold for density matrix eigenvalues [default -1]
  -b [ --balanced ]         rotate the wavefunctions inputN for N>1, so that the overlap <input1|inputN> 
                            is real and positive
  -o [ --output ] arg       output filename [required]
  -v [ --verbose ]          show additional information

By default, the wavefunctions will be summed with zero truncation error, so that the result will have maximum fidelity. To limit the number of states, use the --max-states (or -m) option. To set a given truncation error per site, use --trunc (or -r). To set an eigenvalue cutoff, use --eigen-cutoff (or -d).

The truncation cutoff and eigenvalue cutoff is measured in absolute units, so the wavefunction normalization is important.

The --balanced option is useful for interpolating between two states. For example, if |psi1> and |psi2> are two groundstates with slightly different parameters, then some wavefunction that interpolates between the two will be a good starting vector for DMRG (this is mostly useful if the two wavefunctions belong to the same ordered phase). But to add |psi1> and |psi2> directly, we need to make sure that they have an overlap that is positive. To save having to calculate this ourselves, the --balanced option multiplies the input wavefunctions by a phase angle to make sure that the overlap is real and positive.

Examples

mp-add -v -o result psi1 psi2

This has the effect of {$|\mbox{result}\rangle = |\mbox{psi1}\rangle + |\mbox{psi2}\rangle$}, with no loss of fidelity. The -v option shows some information about the result wavefunction, including the number of states kept at each site, and the truncation error.

mp-add -o result -R 1e-7 --min-states=50 psi1 psi2 psi3

Sum psi1, psi2 and psi3 into result, with an absolute truncation error no worse than {$10^{-7}$} per site, and keeping at least 50 states per site.

[*] Actually, there is probably a term {$L m^3 d^3 n$}, because we calculate the full density matrices when rotating the wavefunctions. This would be improved by using the SVD.