Advanced

Model study of the linear density response function - A comparison between the exact result and RPA

Christiansson, Viktor LU (2017) FYSK02 20171
Department of Physics
Mathematical Physics
Abstract
The time-ordered linear density response function is examined in a model study. Two model dimers are considered; one with one orbital per site and a second one with two orbitals per site. The one-orbital case has U0, the on-site Coulomb interaction, as the only parameter and is solved analytically. The two-orbital case has parameters U0, the upper orbital non-interacting eigenenergy ε1, and the hopping terms t and t0 and is solved numerically. The response function is calculated within the Random-Phase Approximation (RPA) and is compared to the exact results for varied parameters. The general trends found in the study are that RPA seems to get worse for increasing U0 due to the increased localization, and improves for increasing t0... (More)
The time-ordered linear density response function is examined in a model study. Two model dimers are considered; one with one orbital per site and a second one with two orbitals per site. The one-orbital case has U0, the on-site Coulomb interaction, as the only parameter and is solved analytically. The two-orbital case has parameters U0, the upper orbital non-interacting eigenenergy ε1, and the hopping terms t and t0 and is solved numerically. The response function is calculated within the Random-Phase Approximation (RPA) and is compared to the exact results for varied parameters. The general trends found in the study are that RPA seems to get worse for increasing U0 due to the increased localization, and improves for increasing t0 attributed to the increase in delocalization. Furthermore, the two-orbital case was seen to reduce to the on-orbital one for increasing ε1 and in the limit of small t0, which can be used as an analytical check for the correctness of the two-orbital model as it reduces to the one-orbital case which was solved analytically. (Less)
Please use this url to cite or link to this publication:
author
Christiansson, Viktor LU
supervisor
organization
course
FYSK02 20171
year
type
M2 - Bachelor Degree
subject
language
English
id
8915173
date added to LUP
2017-06-14 12:11:33
date last changed
2017-06-14 12:11:33
@misc{8915173,
  abstract     = {The time-ordered linear density response function is examined in a model study. Two model dimers are considered; one with one orbital per site and a second one with two orbitals per site. The one-orbital case has U0, the on-site Coulomb interaction, as the only parameter and is solved analytically. The two-orbital case has parameters U0, the upper orbital non-interacting eigenenergy ε1, and the hopping terms t and t0 and is solved numerically. The response function is calculated within the Random-Phase Approximation (RPA) and is compared to the exact results for varied parameters. The general trends found in the study are that RPA seems to get worse for increasing U0 due to the increased localization, and improves for increasing t0 attributed to the increase in delocalization. Furthermore, the two-orbital case was seen to reduce to the on-orbital one for increasing ε1 and in the limit of small t0, which can be used as an analytical check for the correctness of the two-orbital model as it reduces to the one-orbital case which was solved analytically.},
  author       = {Christiansson, Viktor},
  language     = {eng},
  note         = {Student Paper},
  title        = {Model study of the linear density response function - A comparison between the exact result and RPA},
  year         = {2017},
}