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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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
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.
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
Anyone understand the ground state of AKLT / what I'm missing? @tobiasosborne @AndrewDohertyQu @andrewmchilds @dabacon?
Wow all of those people are way more qualified than I am (esp @AndrewDohertyQu but he's in stealth startup land and won't answer my DMs!) The ground state is simply take spin 1/2 singlets and then project ends of neighboring singlets onto S=1 states?
michael_nielsen Retweeted michael_nielsen
michael_nielsen added,
Sprung!! Sorry Dave about the no reply situation. Mike you are correct about this account of the AKLT state
Mike if you want some other refs to subsequent work would recommend Werner and others CMP paper, Gross and others on the correlation space picture. And the whole literature in “SPT” phases which explains the near degeneracies on the line that you were discussing with Miles
Thanks! I might. I entertained myself yesterday by computing the AKLT ground state explicitly in a couple of different forms. It's an interesting model.
There is this amazing point of view on these states where instead of projecting at sites on maximally entangled pairs between sites, you create it as an open system where the “system”, a qubit for AKLT, interacts unitarily with a sequence of “environments”, spin 1s for AKLT
Is this in those papers you mentioned?
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