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MpWignerEckart

The mp-wigner-eckart command transforms non-abelian symmetries into an abelian subgroup, for example {$SU(2) \supset U(1)$}.

Synopsis

mp-wigner-eckart [options] <symmetry-list> <input-psi> [output-psi]

Options

--help

-f, --force

Description

The mp-wigner-eckart command takes an input wavefunction with at least one {$SU(2)$} symmetry, and projects that symmetry down to {$U(1)$}. If the output file isn't specified, then the reflection is performed in-place, overwriting the old input file.

If the output file already exists, then mp-wigner-eckart will refuse to overwrite it, unless you specify also the --force option.

The symmetry list parameter must match the symmetry list of the original wavefunction, except that every {$SU(2)$} symmetry must be replaced by a {$U(1)$} symmetry. For example, if the original symmetry list is N:U(1),S:SU(2), then the new symmetry list could be N:U(1),Sz:U(1). The name of the new symmetry (Sz in this example) is arbitrary -- normally you would match it to the name of the symmetry in a corresponding lattice.

To find out the symmetry list of an existing wavefunction, use mp-info.

Examples

1. Project an {$SU(2)$} symmetric spin chain to {$U(1)$}.
   
   mp-wigner-eckart "Sz:U(1)" psi1 psi2
   
   If psi2 already exists, then this will fail with an error, leaving the existing file psi2 untouched. To force overwriting psi2, add the -f option.

Restrictions

There are some limitations in the implementation of mp-wigner-eckart in the current version of the toolkit; these will be fixed in the future:

• If the wavefunction has more than one {$SU(2)$} symmetry, then unfortunately it isn't possible to project just one {$SU(2)$} symmetry, all of them need to be projected at the same time.
• The only projection that is currently implemented is {$SU(2) \supset U(1)$}. In the future it is hoped to generalize this to other projections, such as {$SU(2) \supset D_\infty \supset U(1)$}, and {$SU(2) \supset Z_3$}, and {$SU(2) \supset D_\infty \supset Z_2$}.

Notes

This command gets its name from the Wigner-Eckart theorem, which is the basic theorem that underlies the concept of non-abelian MPS.