The mp-reorder-symmetry command performs a reordering or modification of the symmetry list of a wavefunction.
Synopsis
mp-reorder-symmetry [options] <symmetry-list> <input-psi> [output-psi]
Options
--help
show help message
-f, --force
overwrite the output file, if it exists
Description
The mp-reorder-symmetry command takes a symmetry list, and an input wavefunction file, and modifies the symmetry list of the input wavefunction, saving the result to the output file. If the output file isn't specified, then the update is performed in-place, overwriting the old input file.
If the output file already exists, then mp-reorder-symmetry will refuse to overwrite it, unless you specify also the --force option.
Examples
- Reorder the symmetry labels of a wavefunction.
If psi1 has a symmetry list of Sz:U(1),N:U(1), but you want to use operators defined on a Hubbard model lattice that has a symmetry list of N:U(1),Sz:U(1), then use
mp-reorder-symmetry "N:U(1),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.
- Remove the symmetries from a wavefunction
mp-reorder-symmetry "Null:Null" psi1 psi2
- Remove the symmetries from an {$SU(2)$} spin chain. This is a 2-step process as we first need to project the {$SU(2)$} symmetry down to {$U(1)$}.
mp-wigner-eckart "Sz:U(1)" psi1 psi2
mp-reorder-symmetry "Null:Null" psi2
Notes
- The symmetry list of wavefunctions must exactly match the symmetry list of the lattice file, so it is sometimes necessary to reorder the symmetry list as a result of some wavefunction transformation. For example, it might be necessary to reorder
Sz:U(1),N:U(1) into N:U(1),Sz:U(1) in order to reuse an existing Hubbard model lattice file.
- Another use for
mp-reorder-symmetry is for removing quantum numbers in order to apply a transformation or calculate an expectation value that isn't compatible with the original symmetries. For example, given an {$U(1)$} invariant spin chain, to calculate the dihedral group projective symmetry relations for {$\pi$} rotations about the x,y,z axes the symmetry must be removed, because operators such as {$\exp[ i \pi S^x]$} do not commute with {$S^z$}. Quantum numbers can only be removed if the representation has degree 1 (ie, they are abelian, or in the abelian subset of a non-abelian symmetry).
- New quantum numbers can be added to the symmetry list, and they are set to the scalar quantum number.
- The symmetry-list is not allowed to be empty, so if removing all symmetries, use a symmetry-list of
Null:Null.
See also
