Anderson Model & Kondo Hamiltonian - Suggestions & Refs

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SUMMARY

The discussion centers on the relationship between the Anderson model of a localized magnetic impurity and the Kondo Hamiltonian. Participants confirm that the localized magnetic impurity is essential for the Kondo effect and seek mathematical derivations connecting the two models. A recommended reference is J.R. Schriefer and P.A. Wolf's paper published in Phys. Rev. v.149, p.491 (1966), which provides relevant insights into this topic.

PREREQUISITES
  • Understanding of the Anderson model in condensed matter physics
  • Familiarity with the Kondo effect and Kondo Hamiltonian
  • Basic knowledge of many-particle physics
  • Mathematical proficiency in quantum mechanics
NEXT STEPS
  • Study the derivation of the Kondo Hamiltonian from the Anderson model
  • Read Mahan's "Many-Particle Physics" for a comprehensive overview
  • Explore the implications of localized magnetic impurities in quantum systems
  • Investigate other references cited in the discussion for further insights
USEFUL FOR

Physicists, graduate students in condensed matter physics, and researchers interested in the mathematical foundations of the Kondo effect and its relation to the Anderson model.

Lonewolf
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A number of texts claim that the Hamiltonian for the Anderson model of a localised magnetic impurity contains the physics of the Kondo Hamiltonian. Does anyone have any suggestion for how to show this, or any reference that accounts for this?
 
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Er... I don't understand this. Isn't localized magnetic impurity a REQUIREMENT for a Kondo effect?

Zz.
 
Yes, indeed. I'm asking for the maths that takes the Anderson to the Kondo hamiltonian more than the physics, I guess.
 
Ah... I get it now. I'm dreading to look this up in Mahan's "Many-Particle Physics" text. Maybe someone else has a less-tedious way of answering this.

:)

Zz.
 
Oh wait... try this:

J.R. Schriefer and P.A. Wolf, Phys. Rev. v.149, p.491 (1966).

Zz.
 
Thanks a lot for the reference! I'm not sure that it could be any more relevant.
 

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