Abstract
This dissertation investigates the possibilities and limitations of timedependent manybody perturbation theory by studying small Hubbard clusters for which the exact solution is available.
The first part of the thesis is comprised of a short introduction to the
concepts and methodologies used. The second part consists of an review of
the main findings of the thesis and a short summary of four original
papers.
In paper I we study the dynamics of short Hubbard chains within manybody
perturbation theory and compare to the exact solution. The main outcomes are that the Tmatrix approximation works well in the low filling regime and that all approximation which involve correlation effects develop an unphysical steady state.
In paper II we present the methodology used in paper I. We find that the
correlationinduced damping appears even in the presence of leads and
that there are multiple steady and quasi steady states.
In paper III we make a review of the status of time dependent density functional theory for lattice models. In particular we find that a nonperturbative adiabatic local density approximation describes strong correlations well while manybody perturbation theory accounts better for nonadiabatic effects.
In paper IV we propose a method to obtain the double occupancy from the
KadanoffBaym equations. We show that the positiveness condition may be violated in the GW or the second Born approximation but fulfiled in the Tmatrix approximation. We apply this method to obtain the local entanglement entropy.
The first part of the thesis is comprised of a short introduction to the
concepts and methodologies used. The second part consists of an review of
the main findings of the thesis and a short summary of four original
papers.
In paper I we study the dynamics of short Hubbard chains within manybody
perturbation theory and compare to the exact solution. The main outcomes are that the Tmatrix approximation works well in the low filling regime and that all approximation which involve correlation effects develop an unphysical steady state.
In paper II we present the methodology used in paper I. We find that the
correlationinduced damping appears even in the presence of leads and
that there are multiple steady and quasi steady states.
In paper III we make a review of the status of time dependent density functional theory for lattice models. In particular we find that a nonperturbative adiabatic local density approximation describes strong correlations well while manybody perturbation theory accounts better for nonadiabatic effects.
In paper IV we propose a method to obtain the double occupancy from the
KadanoffBaym equations. We show that the positiveness condition may be violated in the GW or the second Born approximation but fulfiled in the Tmatrix approximation. We apply this method to obtain the local entanglement entropy.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2011 May 6 
Print ISBNs  9789174730883 
Publication status  Published  2011 
Bibliographical note
Defence detailsDate: 20110506
Time: 13:15
Place: Lecture Hall A, Sölvegatan 14A, Lund,
External reviewer(s)
Name: Jauho, AnttiPekka
Title: Profesor
Affiliation: Department of Micro and Nanotechnology, DTU Nanotech

Subject classification (UKÄ)
 Condensed Matter Physics
Keywords
 Manybody perturbation theory
 Correlation functions
 Hubbard model
 Nonequilibrium Green's functions
 Fysicumarkivet A:2011:Puig von Friesen