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Holstein Primakoff representation

  1. May 14, 2015 #1
    Holstein Primakoff representation in textbooks is defined by:
    [tex]\hat{S}^+_m=\sqrt{2S}\sqrt{1-\frac{\hat{B}_m^+\hat{B}_m}{2S}}\hat{B}_m[/tex]
    [tex]\hat{S}_m^-=(\hat{S}^+_m)^+[/tex]
    [tex]\hat{S}_m^z=S-\hat{B}_m^+\hat{B}_m[/tex]
    And in practical cases it is often to use binomial series for square root, and condition for that is
    ##\frac{ \langle \hat{B}_m^+\hat{B}_m \rangle}{2S}<<1 ## and because of that I can use binomial series only in case ##S>>\frac{1}{2}##. However, it is very often to use that in case ##S=\frac{1}{2}## in papers. Any explanation?
     
  2. jcsd
  3. May 14, 2015 #2

    DrDu

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    Science Advisor

    The Taylor series for the root still converges well for S=1/2 and ##b^+b=1## or 0 (other values don't occur). Test it yourself.
     
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