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Title: Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons

Abstract

In Part I of this thesis, we study the real part {sigma}({omega}) of the optical conductivity of a repulsive Hubbard ring of circumference L. At zero temperature, and in the absence of disorder, the dc part of {sigma}({omega}) has the form {sigma}({omega}) = (e{sup 2}/h)D{sub c}{delta}({h_bar}{omega}). The charge stiffness D{sub c} tends to a finite, positive value as L {yields} {infinity} in the metallic phase of the model; however, in the Mott-insulating phase of the model, which occurs at a mean electron density n = 1 (half filling), D{sub c} {approximately} O(L{sup 1/2}exp(-L/{xi}(U)) in the large-L limit, which serves to define the localization length {xi} of the nondisordered Mott insulator. We obtain an analytic expression for {xi}(U) as a function of the on-site repulsion U, and show that {xi} is the correlation length of the equal-time single-particle Green`s function, evaluated at half filling. We interpret {xi} as the correlation length of the electron-hole pairing correlations in the ground state of the Mott insulator. We next consider the metallic phase of the model in the vicinity of the metal-insulator transition. We obtain analytic expressions, valid to leading order in the doping {delta} = {vert_bar}1 - n{vert_bar}, for the charge stiffness D{submore » c} = {delta}/{vert_bar}2m{sup *}{vert_bar} and the low-temperature thermopower S = -(k{sup 2}{sub B}T/3e)m{sup *}/{delta}{sup 2} near half filing, where {vert_bar}m{sup *}{vert_bar} is a function of U which we calculate, and sign(m{sup *}) = sign(1 - n). We interpret these results in terms of a physical picture of the charge carriers in the lightly doped Mott insulator as spinless fermionic solitons of size {xi}, effective mass m{sup *}, and number density {delta}, which become noninteracting in the limit {xi}{delta} {yields} 0.« less

Authors:
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
OSTI Identifier:
114807
Resource Type:
Miscellaneous
Resource Relation:
Other Information: TH: Thesis (Ph.D.); PBD: 1992
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; HUBBARD MODEL; ELECTRON CORRELATION; MOTT SCATTERING; EXCITONS; GREEN FUNCTION; ELECTRON-HOLE COUPLING; ELECTRICAL INSULATORS; ELECTRON DENSITY

Citation Formats

Stafford, C A. Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons. United States: N. p., 1992. Web.
Stafford, C A. Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons. United States.
Stafford, C A. Thu . "Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons". United States.
@article{osti_114807,
title = {Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons},
author = {Stafford, C A},
abstractNote = {In Part I of this thesis, we study the real part {sigma}({omega}) of the optical conductivity of a repulsive Hubbard ring of circumference L. At zero temperature, and in the absence of disorder, the dc part of {sigma}({omega}) has the form {sigma}({omega}) = (e{sup 2}/h)D{sub c}{delta}({h_bar}{omega}). The charge stiffness D{sub c} tends to a finite, positive value as L {yields} {infinity} in the metallic phase of the model; however, in the Mott-insulating phase of the model, which occurs at a mean electron density n = 1 (half filling), D{sub c} {approximately} O(L{sup 1/2}exp(-L/{xi}(U)) in the large-L limit, which serves to define the localization length {xi} of the nondisordered Mott insulator. We obtain an analytic expression for {xi}(U) as a function of the on-site repulsion U, and show that {xi} is the correlation length of the equal-time single-particle Green`s function, evaluated at half filling. We interpret {xi} as the correlation length of the electron-hole pairing correlations in the ground state of the Mott insulator. We next consider the metallic phase of the model in the vicinity of the metal-insulator transition. We obtain analytic expressions, valid to leading order in the doping {delta} = {vert_bar}1 - n{vert_bar}, for the charge stiffness D{sub c} = {delta}/{vert_bar}2m{sup *}{vert_bar} and the low-temperature thermopower S = -(k{sup 2}{sub B}T/3e)m{sup *}/{delta}{sup 2} near half filing, where {vert_bar}m{sup *}{vert_bar} is a function of U which we calculate, and sign(m{sup *}) = sign(1 - n). We interpret these results in terms of a physical picture of the charge carriers in the lightly doped Mott insulator as spinless fermionic solitons of size {xi}, effective mass m{sup *}, and number density {delta}, which become noninteracting in the limit {xi}{delta} {yields} 0.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1992},
month = {12}
}

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