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Tools /
## MpShiftBasisThis program shifts the quantum numbers of the local basis of a wavefunction. That is, it changes all quantum numbers {$x$} by {$x \leftarrow x' = x+g$} where {$g$} is a fixed input, and {$+$} here denotes the group operation. This is only well defined if the representation {$g$} has degree 1, and the reduced matrix elements of {$x$} and {$x'$} are the same. This is always true for abelian symmetries, but only sometimes true for non-abelian symmetries. A typical use of this tool is to shift the quantum numbers by 0.5, to convert between a spin representation of {$S^z = \{-1/2, +1/2\}$} and a particle representation of {$N = \{0,1\}$}. Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 802) Compiled on Dec 10 2007 at 11:50:09 usage: mp-shift-basis <quantum-number-name> <shift> <psi> The ## ExamplesSuppose we have a wavefunction Basis has symmetry Sz:U(1), size = 2 N QuantumNumber 0 -0.5 1 0.5 To shift the quantum numbers to a particle representation (ie. spinless fermions), use mp-shift Sz 0.5 psi This gives a new local basis of Basis has symmetry Sz:U(1), size = 2 N QuantumNumber 0 0 1 1 ## NotesTo be able to use the resulting wavefunction with lattice files defined for a particle number symmetry, one more step is needed to rename the 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 ## See Also |

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