# Anderson Model & Kondo Hamiltonian - Suggestions & Refs

• Lonewolf
In summary, the conversation discusses the connection between the Hamiltonian for the Anderson model of a localised magnetic impurity and the Kondo Hamiltonian. The participants are looking for mathematical evidence or references to support this claim. Eventually, a relevant reference is suggested by one of the participants.
Lonewolf
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?

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.

## 1. What is the Anderson Model?

The Anderson Model is a theoretical model used to describe the behavior of electrons in a solid material. It was developed by physicist Philip W. Anderson in 1961 and has been widely used in condensed matter physics to study the properties of metals and insulators.

## 2. What is the Kondo Hamiltonian?

The Kondo Hamiltonian is a mathematical model used to describe the interaction between a localized spin and the conduction electrons in a metal. It was first proposed by physicist Jun Kondo in 1964 and has been used to study the phenomenon of Kondo effect, which describes the scattering of conduction electrons by localized magnetic impurities in a metal.

## 3. How are the Anderson Model and Kondo Hamiltonian related?

The Anderson Model and Kondo Hamiltonian are related in that they both describe the behavior of electrons in a solid material. The Anderson Model is a more general model that can be used to study the properties of a wide range of materials, while the Kondo Hamiltonian is a specific model that focuses on the interaction between a localized spin and conduction electrons in a metal.

## 4. What are some suggestions for studying the Anderson Model and Kondo Hamiltonian?

Some suggestions for studying the Anderson Model and Kondo Hamiltonian include reading textbooks and research papers on the topic, attending lectures or seminars by experts in the field, and performing computational simulations to better understand the behavior of these models. Additionally, collaborating with other scientists and discussing ideas can also be helpful in gaining a deeper understanding of these models.

## 5. Can you provide some references for further reading on the Anderson Model and Kondo Hamiltonian?

Some references for further reading on the Anderson Model and Kondo Hamiltonian include the original papers by Philip W. Anderson and Jun Kondo, as well as textbooks such as "Introduction to Solid State Physics" by Charles Kittel and "Condensed Matter Field Theory" by Alexander Altland and Ben Simons. Additionally, there are many research papers and review articles published on these topics in scientific journals such as Physical Review Letters and Reviews of Modern Physics.

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