In Chapter 1, we introduce the physics of the HTSC, starting with an historical
overview of the problem and describing some experimental results that
characterize these materials. Subsequently, we introduce the t−J model,
which allows a microscopic description of the HTSC and we introduce the
Resonating Valence Bond (RVB) wave function.
In Chapter 2, we will describe the numerical techniques used for obtaining
the results of our thesis. We start from the Lanczos method, that enable
us to obtain exact results for small cluster size and then we enter in the
topic of the quantum Monte Carlo technique. We describe the variational
Monte Carlo method, the optimization algorithm and we will introduce the
Green’s function Monte Carlo and fixed-node approximation, that improve
the variational results.
In Chapter 3, we will introduce our new variational wave function which
generalizes the RVB state we show our results on the charge fluctuations
(phase separation problem) for the two-dimensional t−J model. The main
results of this chapter has been published in Physical Review B [7].
In Chapter 4, we will study the magnetic and superconducting properties
of the two-dimensional t−J and t−t′−J model, trying to understand the
role of the next-nearest-neighbor hopping term on the magnetic and superconducting
phases. We will show a phase diagram of the magnetic and superconducting
correlations, which qualitatively reproduce the actual phase
diagram of HTSC and gives some indication on the origin of the electronic
pairing. The main results of this chapter were submitted to Physical Review
B [8].
