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Acknowledgments
The biggest thank goes to Frédéric Mila and Thierry Giamarchi, who gave me the
opportunity to engage a doctoral thesis at IRRMA. Special thanks goes also to
Andreas Martin Lauechli. I am grateful not only for their scientific guidance, but
also for their effort to make our discussions very alive and more generally for the
nice time that I spent in the respective groups of Irrma, UniGe and ITP-EPFL.
During these four years and a half, they were particularly involved in all the
work done in the chapters presented in this dissertation. Moreover, I had also
the chance to collaborate and discuss with other distinguished physicists. I am
especially thinking to Michel Ferrero and Federico Becca, with whom I spent some
nice time at the Sissa (Trieste, Italy). I also enjoyed working in collaboration with
Didier Poilblanc and Sylvain Caponi (Irsamc, Toulouse, France), that have hosted
me very nicely in Toulouse for a short visit. I also thank a lot Claudius Gross
and Walter Hofstetter (Frankfurt, Germany) that have allowed me to come and
visit them in Frankfurt. The scientific discussions were very motivating. Special
thanks also to Werner Krauth (Paris) who explained to me the scientific activity
of his group. Finally, I would like to thank Chandra Varma (Irvine, USA) for
past and ongoing discussions related to the presence of orbital currents in the
pseudogap phase of the cuprates. I detail here further who was involved in the
work of the chapters of the dissertation:
Chapter 3: I am very grateful to Michel Ferrero and Federico Becca for discussions
about the Pfaffians, that are used to sample the wave-function having noncollinear
magnetism.
Chapter 4: The credits of the RVB mean field theory in this chapter is entirely due
to Thomas Gloor. Moreover, the quantum Monte-Carlo results, shown in
this chapter as a comparison with the variational Monte-Carlo results, were
done by the work of Thomas Gloor and Andreas Martin Laeuchli.
Chapter 5: This was a collaboration with Didier Poilblanc and Sylvain Caponi. Everything
related to the mean-field calculations done in this chapter is due to
their impressive work.
Chapter 6: I could profit from the experience of Andreas Laeuchli, who helped me to
understand in details the exact diagonalization calculations. We could also
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