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I Rényi entropy becomes von Neumann entropy

  1. Mar 19, 2017 #1
    In holographic entanglement entropy notes like here, they let alpha go to one in (2.41) and get (2.42). But (2.41) goes towards infinity, when doing that! Can someone explain how alpha --> 1 will make (2.41) into (2.42)? Thank you!

    Renyi Neumann.PNG
     
  2. jcsd
  3. Mar 19, 2017 #2

    ShayanJ

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    You should keep in mind that ## Tr \rho=1 ##. So ## \displaystyle \lim_{\alpha \to 1} \log(Tr \rho^\alpha)=0##. So ## \displaystyle \lim_{\alpha \to 1}S_\alpha(\rho)=\frac 0 0 ## and is indeterminate. To calculate it, you need to use L'Hopital's rule and differentiate the numerator and denominator w.r.t. ## \alpha ## and then take the limit.
     
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