@phdthesis{Guenther2010, author = {G{\"u}nther, Falk}, title = {Pair correlations from symmetry-broken states in strongly correlated electronic systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus-19631}, school = {BTU Cottbus - Senftenberg}, year = {2010}, abstract = {As a result of 20 years of experimental and theoretical investigations of high temperature superconductors (HTSC) one can draw a very complex and rich phase diagram that cannot be described completely yet. Numerous experimental findings give strong hints for an inhomogeneous distribution of spin and charge correlations in HTSC. Motivated by the experimental findings we try to answer the question whether pair correlations from broken symmetry states can be found in the framework of the Gutzwiller approximation of the Hubbard model.After an introductory discussion of selected experimental works and theoretical models we derive the charge-rotationally invariant Gutzwiller functional for the one-band Hubbard model. On this basis we calculate various states from the saddle point solution of functional in the attractive (U<0) regime. Starting with a second order expansion we investigate the instability of a normal system towards SC in the framework of the time dependent Gutzwiller approximation (TDGA). We derive criteria for a phase transition from the normal to the superconducting phase in the paramagnetic regime. We show results for an infinite dimensional lattice that are in good agreement with QMC data. In the next section of this work we present results for finite dimensional systems. We compare numerical results from the GA with the conventional Hartree-Fock approximation. As an example we discuss a homogeneously superconducting and a charge-ordered state. We show that the difference is mainly in the crossover from weak to strong coupling which is due to the renormalization in the Gutzwiller formalism. In a next step we derive an effective Hamiltonian on top of the saddle point solution. We compare the formalism analytically with the findings from the well known BCS theory. We verify our conclusions by numerical calculations. Motivated by different experimental works on d-wave symmetric k-dependent SC gaps we focus on the question whether states including non-local pair correlations can be a solution of the GA and how does this correlation lower the energy.We restrict to the repulsive regime (U>0) and discuss the formal requirements for a possible solution in view of a coexisting spin order and the interplay of local and non-local pair order. As a next application we prepare inhomogeneous solutions in the normal and in the extended Hubbard model where we include an additional inter-site interaction by the parameter V>0. We present inhomogeneous solutions that are characterized by stripe-shaped domains where the parameters for charge- and pair- ordering change their phases or their amplitude. We obtain results for the normal and the extended Hubbard model and we discuss the influence of the parameter V. We show that in case of V>0 a pair density wave (PDW) without stripes is the ground state. Another focus of the work is on point-like inhomogeneities namely polarons and (anti-)vortices in finite clusters. We present results that show a good agreement with the logarithmic dependence of the energy of the vortex state with respect to the vortex radius as well as possible attraction between vortex and anti-vortices. Finally in the last chapter we introduce the superfluid density in order to discuss the stability of our solutions in finite dimensional systems. We give a short overview on different analytical approaches to this quantity. We present an approach that is based on an energy expansion view of an angular distortion of the charge vector field. We discuss this approach by comparing the numerical GA results with exact QMC results where our approach turned out to be in good qualitative agreement.}, subject = {Elektronenkorrelation; Hubbard-Modell; Festk{\"o}rperphysik; Korrelierte Elektronensysteme; Attraktives Hubbardmodell; Solid state physics; Correlated electronic systems; Attractive Hubbard model}, language = {en} } @phdthesis{BaronvonOelsen2012, author = {Baron von Oelsen, Ernst}, title = {The time-dependent Gutzwiller Approximation for Multi-Band Hubbard Models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus-25206}, school = {BTU Cottbus - Senftenberg}, year = {2012}, abstract = {We formulate a generalization of the time-dependent Gutzwiller theory for the application to multi-band Hubbard models. Our approach allows for the computation of general momentum- and frequency-dependent two-particle response functions. The in-depth knowledge of them is crucial for the understanding and interpretation of experiments in solid-state physics. In the calculation of ground-state properties of Hubbard models, the Gutzwiller approach is known to overcome the main shortcomings of the Hartree-Fock approximation, whose time-dependent generalization is the standard text-book method for the calculation of response functions. We therefore expect that the time-dependent Gutzwiller theory, that has been formulated only for the single-band Hubbard model so far, will offer a technique yielding new insight into the dynamics of strongly-correlated multi-orbital systems. In this thesis, we motivate the employment of multi-orbital Hubbard models and give an introduction to multi-band Hubbard models in Chapters 1 and 2. Their treatment within the Gutzwiller variational approach is subject of Chapter 3, where it is supplemented by investigations that connect our new approach to previous results. We derive the random-phase approximation as the time-dependent Hartree-Fock theory in Chapter 4, followed by the derivation of the corresponding time-dependent Gutzwiller theory in Chapter 5. We demonstrate the applicability of our new approach in Chapter 6, where we calculate the transversal spin susceptibility of a Hubbard model with two degenerate bands and present numerical results for systems in infinite and three spatial dimensions. A summary and conclusion is given in the final Chapter. Mathematical details of our derivations are presented in several appendices.}, subject = {Hubbard-Modell; Zeitabh{\"a}ngige Methode; Stochastische Approximation; Zeitabh{\"a}ngige Gutzwiller-N{\"a}herung; Mehr-Band Hubbard Modelle; Spinsuszeptibilit{\"a}t; Time-dependent; Gutzwiller; Multi-Band Hubbard Models; Spin susceptibility}, language = {en} }