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https://hdl.handle.net/2142/19406
Description
Title
Bosonization in 1 + 1/2 dimensions
Author(s)
Fuentes, Manuel Alejandro
Issue Date
1995
Doctoral Committee Chair(s)
Fradkin, Eduardo H.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
In this thesis we derive a set of bosonization rules for the problem of a fermionic interacting system living on the half line coupled to a quantum degree of freedom at a boundary. This is an appropriate model to describe the physics of an electronic system in quantum wires with impurities. First we derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.
We also consider a system of free fermions in the half line coupled to a backscattering amplitude at the boundary. We calculate the exact effective action for general backscattering amplitudes. The action also includes the effects of both a (time-dependent) forward scattering amplitude and a dynamical chiral twist of the fermion boundary conditions. For a small backscattering amplitude, the effective action has the expected boundary Sine-Gordon form. We discuss applications of our results to one-dimensional Fermi systems with local backscattering.
Finally, we study the Luttinger-Thirring model in one space dimension coupled to a quantum impurity at the origin. We generalize the bosonization methods developed for the free fermions, to study the effects of interactions on fermi systems coupled to impurities. Special attention is given to the role of the fermion boundary conditions on the bosonized effective theory. We apply our results to the study of the induced charge at the boundary. Using this result, we analyze the interplay between the boundary degree of freedom and the interaction. We give detail discussion of the properties of the one- particle green function (relevant for tunneling problems).
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