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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A few tidbits: the model is spin s=1. The s=1 spins in the chain are modelled as the symmetric subspace of 2 spin 1/2 particles, i.e., the space spanned by ^^, vv, and ^v+v^, in an obvious notation.
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It seems that we should think of the bonds between dots in the image as being like spin 1/2 singlets, ^v-v^. So this wld be s'thing like: *(^v-v^)(^v-v^)*, where the two * states are to be specified. But I don't see how to choose the *s so these are in the right sym. subspacespic.twitter.com/TJQXWnai06
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Anyone understand the ground state of AKLT / what I'm missing?
@tobiasosborne@AndrewDohertyQu@andrewmchilds@dabacon?Show this thread -
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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!)
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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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let us know when you exit the wormhole..
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