Trying to understand the ground state of the AKLT model, and having trouble parsing the paper. Here's how it's described in the famous AKLT paper, and the corresponding Hamiltonian:pic.twitter.com/wv9iEBF1k5
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Does the definition of the projector (oval shaped symbol) on this page help answer your question about what * should be? https://en.m.wikipedia.org/wiki/AKLT_model (I did that write up for Wikipedia because it’s such an interesting model and I was surprised it wasn’t already on there!)
I'm afraid I found that unclear. Is it saying that you construct the product of the spin singlet states, and then project onto the symmetric subspace of the paired spin 1/2's?
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So in the case of n = 3 spin 1's, represented as 6 spin 1/2s, the ground state would be in P^{otimes 3} * otimes s otimes s otimes *, where P projects on the symmetric subpace of two spin 1/2s, s is the usual spin singlet ^v-v^, and the * states are arbitrary spin 1/2 states.
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It seems unclear why the ground state is two-dimensional, since the end spins both have 2 unspecified degrees of freedom.
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Yes, starting from product of the singlets ^^ becomes the “+” (topmost) S=1 state where the left ^ is from the left-hand singlet and the right ^ is from the right-hand singlet (singlets are bonds; S=1’s are sites). vv becomes “-“. And (^v+v^) becomes “0” (Sz=0 state of the S=1)
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