Path integral methods for the large-N Kondo model

A path integral formulation of the SU(N) Kondo model is explored as a possible theoretical tool for studying generalizations of the model, such as the Kondo lattice, which are difficult to study by other means. Saddle point approximations to the path integral lead to an expansion in powers of 1/N. After developing the basic path integral formalism, the method is applied to three related problems. The first of these is an exactly soluble toy model which, like the Kondo model, shows smooth crossover between weakly mixed configurations at high energy scales and strongly mixed singlet configurations at low energy scales. Simple approximations are found for describing the high and low temperature limits of the model, and the failure of these approximations in the crossover region is interpreted in terms of differences between the high and low energy scales. In chapter 4 the low temperature approximation is used to study the Kondo crossover as a function of magnetic field at zero temperature. Smooth and plausible crossover is found provided the magnetic field is introduced in a way which preserves degeneracy proportional toN, indicating that the failure to describe temperature crossover is not a general limitation of the method. Finally, the same zero temperature equations are generalized in chapter 5 to a model of a magnetic impurity interacting with a gapless electronic band. Using a simple renormalization group argument this model is shown to have a transition as a function of coupling constant at zero temperature. This result is confirmed and extended using the zero temperature path integral equations, and certain special features of the magnetic field crossover are noted.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Withoff, David John

Contributors dc:contributor

• Fradkin, Eduardo H.

• path integral methods
• Kondo model

Statement dc:rights

• ©1988 Withoff

Language dc:language

en

Identifier

3473911

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30683