The generic phase diagram of lightly hole doped high-
Tc cuprates hosts an antiferromagnetic insulating phase with well-defined spin-wave excitations. Contrary to the weak-coupling prediction, these modes persist up to the overdoped metallic regime as intense and dispersive paramagnons. Here we report on our study of the low-energy magnetic and charge excitations within the extended Hubbard model at strong coupling, using a modified
1/N expansion method with a variational state serving as the saddle point solution. Despite clear separation of magnetic and Hubbard-
U energy scales, we find that incipient Mottness affects qualitatively dispersions and widths of magnetic modes throughout the entire phase diagram. The obtained magnetic and charge dynamical structure factors agree semiquantitatively with recent resonant x-ray and neutron scattering data for ${\mathrm{La}}_{2\ensuremath{-}\mathit{x}}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{CuO}}_{4}$ and ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ at all available doping levels. The weak-coupling random-phase approximation fails already for underdoped samples, pointing to the nontrivial intertwining of distinct energy scales in cuprate superconductors. The existence of a discrete charge mode which splits off the electron-hole continuum is also predicted.
The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.
The discovery of high-Tc superconductivity in the cuprates, and the observation that strong correlations are important in connection with these compounds has led to a tremendous interest in understanding the physics of strongly correlated electronic models. In particular the two simplest models for strongly correlated electrons, namely the Hubbard and t–J models, have been the subject of intensive studies. In a milestone paper of 1987, P.W. Anderson proposed that a resonating valence bond (RVB) wave-function, which consists of a superposition of valence-bond states, contains the ingredients to account for a consistent theory of the Hubbard and t–J models. Motivated by the success of variational Monte- Carlo to describe some of the peculiar properties of the cuprates, we propose in this dissertation, on one hand, to extend the method to further strongly correlated models to describe other compounds such as graphene, carbon nanotube or the cobaltite compounds, and on the other hand we propose to focus on the pseudo-gap phase of the cuprates, which is still prompting for a consistent theory. In particular, the issue of checkerboard spatial modulations in the density of states in the low temperature regime of the cuprates is addressed. Finally, we have studied the possibility for spontaneous orbital currents in the cuprates, that might play a key role in the theory of high Tc superconductors.