Holstein Primakoff representation

In summary, Holstein Primakoff representation in textbooks defines the operators \hat{S}^+_m, \hat{S}_m^-, and \hat{S}_m^z in terms of the operators \hat{B}_m^+ and \hat{B}_m. In practical cases, the binomial series is often used for the square root, but only when the condition \frac{ \langle \hat{B}_m^+\hat{B}_m \rangle}{2S}<<1 is met, which is typically the case when S>\frac{1}{2}. However, it has been observed that the Taylor series for the root still converges well for S=\frac{1}{
  • #1
LagrangeEuler
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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?
 
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  • #2
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.
 

What is Holstein Primakoff representation?

Holstein-Primakoff representation is a mathematical technique used in quantum mechanics to describe the behavior of spin systems. It allows for the representation of spin operators as bosonic creation and annihilation operators, making calculations easier to perform.

What is the significance of Holstein Primakoff representation?

The significance of Holstein-Primakoff representation lies in its ability to simplify calculations for spin systems, making them more tractable and allowing for the prediction of various physical properties of these systems.

How is Holstein Primakoff representation used in research?

Holstein-Primakoff representation is used in a variety of research areas, including quantum computing, condensed matter physics, and quantum information theory. It is particularly useful in studying magnetic materials and their properties.

What are the limitations of Holstein Primakoff representation?

The main limitation of Holstein-Primakoff representation is that it only applies to systems with large spin values, typically greater than or equal to 1/2. It also does not take into account interactions between individual spins, which may be important in some systems.

Can Holstein Primakoff representation be extended to other systems?

Yes, Holstein-Primakoff representation has been extended to various systems beyond spin systems, such as systems with higher spin values and systems with multiple types of particles. However, its applicability may still be limited in certain cases.

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