Matrix Product Toolkit | Tools / MpScaleBasis

This program scales the quantum numbers of a {$U(1)$} symmetry by a constant factor. This is useful for converting between pseudospin and particle representations, for example.

Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 802)
Compiled on Dec 10 2007 at 11:50:17
usage: mp-scale-basis <quantum-number-name> <factor> <psi>
this is applicable only to U(1) quantum numbers.

The multiplicative factor can be any real number, but if it is not an integer then you must be sure that the resulting quantum numbers satisfy the correct sum rules.

Examples

To scale the Sz quantum numbers of a wavefunction psi by a factor 2, use

mp-scale-basis Sz 2 psi

The reverse operation is well-defined, and is achieved by

mp-scale-basis Sz 0.5 psi

Notes

Note however that scaling by a fraction might lead to trouble, as the quantum numbers will be rounded to the nearest half-integer and might not satisfy the correct sum rules anymore. Scaling by zero should work and would have the effect of setting all quantum numbers to zero, effectively removing that symmetry. This could be useful, for example, to apply a symmetry breaking perturbation to an initially symmetric state.

This program applies the transformation to all sites of the lattice. It would be easy to apply the transformation to only a single site, or a selection - the only question is what format to use to specify this on the command line.

To see what the quantum numbers of the local basis are, use mp-info -b psi.

MpScaleBasis

Examples

Notes

See Also