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michael_nielsen's profile
michael_nielsen
michael_nielsen
michael_nielsen
@michael_nielsen

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michael_nielsen

@michael_nielsen

Searching for the numinous. Co-purveyor of https://quantum.country/ 

San Francisco, CA
michaelnielsen.org
Joined July 2008

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    1. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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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

      1 reply 0 retweets 23 likes
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    2. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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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.

      1 reply 0 retweets 3 likes
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    3. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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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

      3 replies 0 retweets 4 likes
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    4. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      Anyone understand the ground state of AKLT / what I'm missing? @tobiasosborne @AndrewDohertyQu @andrewmchilds @dabacon?

      3 replies 0 retweets 1 like
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    5. dabacon‏ @dabacon 28 Sep 2018
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      Replying to @michael_nielsen @tobiasosborne and

      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?

      1 reply 0 retweets 3 likes
      michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      Replying to @dabacon @tobiasosborne and

      michael_nielsen Retweeted michael_nielsen

      This, I guess?https://twitter.com/michael_nielsen/status/1045863881292242945 …

      michael_nielsen added,

      michael_nielsen @michael_nielsen
      Replying to @MStoudenmire
      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?
      10:10 PM - 28 Sep 2018
      1 reply 0 retweets 0 likes
        1. New conversation
        1. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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          Replying to @michael_nielsen @dabacon and

          Sprung!! Sorry Dave about the no reply situation. Mike you are correct about this account of the AKLT state

          2 replies 0 retweets 1 like
        2. michael_nielsen‏ @michael_nielsen 3 Oct 2018
          • Report Tweet
          Replying to @AndrewDohertyQu @dabacon and

          While you're here: are you in the Bay Area now? If so, lunch dinner etc would be great!

          1 reply 0 retweets 0 likes
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