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  A simple question on the projected wave function?

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For example, consider a spin-1/2 AFM Heisenberg Hamiltonian H=<ij>SiSj, and we perform a Schwinger-fermion(Si=12fiσfi) mean-field study.

Let HMF=<ij>(fiχijfj+fiηijfj+H.c.) be the resulting mean-field Hamiltonian, where (χij,ηij) is the mean-field ansatz. And let ψ1,2 represent two exact eigenstates of HMF with energies E1,2(E1>E2), say HMFψ1,2=E1,2ψ1,2.

Now we can construct the physical spin states ϕ1,2 by applying the projective operator P=i(2ˆniˆn2i)(Note that Pi(1ˆniˆni)) to ψ1,2(where ˆni=fifi+fifi), say ϕ1,2=Pψ1,2, and generally we don't expect that ϕ1,2 are the exact eigenstates of the original spin Hamiltonian H.

My question is: ϕ1Hϕ1ϕ1ϕ1>ϕ2Hϕ2ϕ2ϕ2 ? If it's true, then how to prove it rigorously ? Thanks a lot.


This post imported from StackExchange Physics at 2014-03-09 08:43 (UCT), posted by SE-user K-boy

asked Aug 31, 2013 in Theoretical Physics by Kai Li (980 points) [ revision history ]
retagged Mar 25, 2014 by dimension10
Too much quantities are not defined precisely, and no reference is given, so you had better to completely rewrite your question, or to ask a new question.

This post imported from StackExchange Physics at 2014-03-09 08:43 (UCT), posted by SE-user Trimok
@ Trimok, I added some details to my post.

This post imported from StackExchange Physics at 2014-03-09 08:43 (UCT), posted by SE-user K-boy

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