What you know you can't explain, but you feel it. You've felt it your entire life, that there's something wrong with the world. You don't know what it is, but it's there, like a splinter in your mind, driving you mad.
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 |