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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
    6. 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?
      1 reply 0 retweets 0 likes
    7. 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
    8. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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      Replying to @AndrewDohertyQu @michael_nielsen and

      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

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

      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.

      1 reply 0 retweets 2 likes
    10. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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      Replying to @michael_nielsen @dabacon and

      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

      1 reply 0 retweets 2 likes
      michael_nielsen‏ @michael_nielsen 3 Oct 2018
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      Replying to @AndrewDohertyQu @dabacon and

      Is this in those papers you mentioned?

      9:15 PM - 3 Oct 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

          I think might be in the Werner one but hard to extract. Take a look at section 5 of this review and references therein https://arxiv.org/pdf/quant-ph/0608197.pdf …

          1 reply 0 retweets 1 like
        2. michael_nielsen‏ @michael_nielsen 3 Oct 2018
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          Replying to @AndrewDohertyQu @dabacon and

          Thanks!

          0 replies 0 retweets 0 likes
          3. End of conversation

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