Tools /
## MpWignerEckartOldThis program projects non-abelian quantum numbers onto the `axis of quantization', thereby breaking the symmetry down into an abelian subgroup. Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 802) Compiled on Dec 10 2007 at 11:49:00 usage: mp-wigner-eckart <input-psi> <output-psi> <symmetry-list> <projection> The new The ## ExamplesFor the Hubbard model with {$SO(4) \equiv SU(2) \otimes SU(2)$} symmetry, we have the symmetry list The projection quantum numbers can be chosen arbitrarily, provided that {$-Q \leq Q^z \leq Q$} and {$-S \leq S^z \leq S$}, and {$Q+Q^z$} and {$S+S^z$} are both integer (ie, if {$Q$} or {$S$} are (half-)integer, then {$Q^z$} and {$S^z$} are also (half-)integer). For example, for a state mp-wigner-eckart psi-in psi-out "Qz:U(1),Sz:U(1)" -4,2 Note that the z-component of the pseudospin is related to the particle number by {$Q^z = \frac{N-1}{2}$}. Thus, {$Q^z=0$} corresponds to half-filling, and if {$Q > 0$}, the {$Q^z = 0$} state is a half-filled excited state. The hole-doped and particle-doped groundstates correspond to {$Q^z = -Q$} and {$Q^z = Q$} respectively. To convert from {$Q^z$} to the particle number, a shift, scale, and rename (and possibly a reordering of the basis) is required. ## See Also |

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