Model study of the linear density response function - A comparison between the exact result and RPA
(2017) FYSK02 20171Department 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:
http://lup.lub.lu.se/student-papers/record/8915173
- author
- Christiansson, Viktor LU
- supervisor
- organization
- course
- FYSK02 20171
- year
- 2017
- 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}}, }