@phdthesis{Martens2024, author = {Martens, Christian}, title = {A study of the charge and spin order dynamics for cuprate superconductors : a Gutzwiller analysis for the single-band Hubbard model}, doi = {10.26127/BTUOpen-7194}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-71945}, school = {BTU Cottbus - Senftenberg}, year = {2024}, abstract = {In recent years, the role of charge density waves (CDW) in the study of high-temperature superconductors, such as cuprates and nickelates, has gained importance, so that CDW can provide potential insights into the mechanism of high-temperature superconductivity. Cuprates and nickelates are transition metals and have their valence electrons in the d-orbitals, which makes them belong to the family of correlated materials. In the past, a variety of experimental techniques, such as X-ray scattering and neutron scattering, have been performed to better understand such materials and the electronic properties of CDWs and spin-density waves (SDWs), which are thought to be connected to high-temperature superconductivity. However, the exact nature of CDW, SDW is not yet fully understood. Often correlated materials are described with the so-called multi-band Hubbard model, which takes into account the Coulomb interactions in d- or f-orbitals with a local parameter U. In the structure of the cuprate high-temperature superconductor LCO, the low-energy electron structure of the CuO2 planes is of interest, as this is where CDW, SDW and 2D high-temperature superconductivity take place. For this reason, the 3-band Hubbard model is often used, which takes into account the interaction of the Cu and O orbitals. Here we describe the time-dependent Gutzwiller approximation (TDGA) for the single-band Hubbard model. The description of a single-band construct for the Hubbard model was discussed in the work of Zhang and Rice, where they assume a hybridisation of the copper atom with the neighbouring oxygen atoms inside the unit cell forming a singlet state. While the Gutzwiller approximation can be solved analytically in one dimension using the Bethe ansatz, for real systems one has to resort either to the exact diagonalisation of small clusters or to approximation methods. We analyse the non-equilibrium dynamics of the electron structure in comparison to the optical conductivity in the linear response and non-equilibrium case. The starting point is the half-filled antiferromagnetic (AF) state, which is forms in LCO at weak hole doping p and allows the description of the stripe state by introducing hole doping near zero temperature. The focus here is on the site-centered and bond-centered stripe states characterized by a domain wall, which possesses an accumulation of hole doping and inverts the spin order. The results of the TDGA are compared with those of the time-dependent Hartree-Fock approximation (TDHF) and, in the case of the stripe states, also with the time-dependent Landau theory (TDL).}, subject = {Charge stripes; Spin stripes; Time-dependent Gutzwiller approximation; Single-band Hubbard model; Zeitabh{\"a}ngige Gutzwiller-Approximation; Ladungs-Stripes; Spin-Stripes; Einband-Hubbard-Modell; Hochtemperatursupraleitung; Cuprate; Ladungsdichtewelle; Spindichtewelle; Elektronenstruktur}, language = {en} }