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https://hdl.handle.net/2142/30683
Description
Title
Path integral methods for the large-N Kondo model
Author(s)
Withoff, David John
Issue Date
1988
Doctoral Committee Chair(s)
Fradkin, Eduardo H.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
path integral methods
Kondo model
Language
en
Abstract
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.
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