pdf, 9 MiB - Infoscience - EPFL

Abstract
The discovery of high-T c 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 T c superconductors.
Keywords : Superconductivity, Electronic correlation, Cuprates, Lattice Theories,
Variational Methods, Low Energy Physics, Monte-Carlo simulations.
3