Development of the new functional integral formalism and its application to the periodic Anderson model.
Item
-
Title
-
Development of the new functional integral formalism and its application to the periodic Anderson model.
-
Identifier
-
AAI9009792
-
identifier
-
9009792
-
Creator
-
Tolpin, Anatoly Emiljevich.
-
Contributor
-
Adviser: Joseph L. Birman
-
Date
-
1989
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Physics, Condensed Matter
-
Abstract
-
A new approach was developed to the problem of the propagator construction within the framework of the functional integral formalism. Central to this approach is the definition of a local operator construction, which defines the operators over some field(s) as being dependent on field(s) variables. This is in contrast to the usual creation and annihilation operators, which in the present context are defined as "global" operators. The relation to the standard functional integral formalism has been investigated, and the problem of the discontinuous paths in the standard functional integral formalism has been resolved. One simple application of the new formalism to the linear harmonic oscillator problem is also discussed.;The new functional integral formalism has been used to study the orbitally nondegenerate periodic Anderson problem. A smooth second-order like transition behavior around T{dollar}\sb{lcub}\rm K{rcub}{dollar} has been obtained. Various saddle points, including the one corresponding to the Kondo resonance have been derived. However no stable state corresponding to the Heavy Fermion regime has been found.;The new functional integral formalism has been further applied to the degenerate lattice Anderson Hamiltonian in the Kondo regime. It has been recognized that in the coherent low temperature regime operators in the effective Hamiltonian belong to an SU(2{dollar}J{dollar} + 2) dynamical algebra. Subsequently a canonical transformation has been performed that decouples the quasiparticle branches, thereby setting up the so-called decoupling equation. It turns out that the decoupling equation has a solution of the symmetry-breaking type. The thermodynamic response functions and other quantities were calculated for this symmetry-breaking state. This solution is a consequence of the degeneracy of the uncoupled f-orbitals. The solution is characterized by the interatomic hopping of f-electrons, which produces the spin delocalization regime and pins the renormalized f-level close to the Fermi level. It is believed that this new state forms a correct description of the Heavy Fermion state at low temperatures.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
