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 timeordered 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 oneorbital case has U0, the onsite Coulomb interaction, as the only parameter and is solved analytically. The twoorbital case has parameters U0, the upper orbital noninteracting eigenenergy ε1, and the hopping terms t and t0 and is solved numerically. The response function is calculated within the RandomPhase 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 timeordered 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 oneorbital case has U0, the onsite Coulomb interaction, as the only parameter and is solved analytically. The twoorbital case has parameters U0, the upper orbital noninteracting eigenenergy ε1, and the hopping terms t and t0 and is solved numerically. The response function is calculated within the RandomPhase 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 twoorbital case was seen to reduce to the onorbital one for increasing ε1 and in the limit of small t0, which can be used as an analytical check for the correctness of the twoorbital model as it reduces to the oneorbital case which was solved analytically. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8915173
 author
 Christiansson, Viktor ^{LU}
 supervisor

 Ferdi Aryasetiawan ^{LU}
 organization
 course
 FYSK02 20171
 year
 2017
 type
 M2  Bachelor Degree
 subject
 language
 English
 id
 8915173
 date added to LUP
 20170614 12:11:33
 date last changed
 20170614 12:11:33
@misc{8915173, abstract = {The timeordered 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 oneorbital case has U0, the onsite Coulomb interaction, as the only parameter and is solved analytically. The twoorbital case has parameters U0, the upper orbital noninteracting eigenenergy ε1, and the hopping terms t and t0 and is solved numerically. The response function is calculated within the RandomPhase 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 twoorbital case was seen to reduce to the onorbital one for increasing ε1 and in the limit of small t0, which can be used as an analytical check for the correctness of the twoorbital model as it reduces to the oneorbital 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}, }