The thesis is organized as follows:
• In chapter 1, we introduce the key concepts of Mott insulator and spin liquid, focusing, in particular, on the property of a spin-liquid phase. We also present the main experiments where a Mott insulating and, especially, a spin-liquid behaviour has been observed. The chapter closes with a detailed description of the Hubbard and the Heisenberg Hamiltonians, which can capture the physics of strongly-correlated electron systems.
• In chapter 2, we introduce the electronic wave functions use d to approximate the exact ground state of correlated models. We focus in particular on backflow correlations, that we apply, for the first time, on a lattice model. Moreover, we introduce the numerical techniques used in this thesis. We describe the Variational Monte Carlo method, the optimization algorithm and Green’s Function Monte Carlo with the fixed-node approximation. In the last part of the chapter, we compare our results for the Hubbard model with the exact ones on small lattice sizes and with other established approaches.
• In chapter 3, we present our phase diagram for the Hubbard model on the square lattice with nearest and next-nearest neighbour couplings. A particular emphasis is given on the spin liquid phase,
we can stabilize at strong coupling and large enough frustration, by means of backflow correlations. Our results are compared with the other ones existing in literature.
• In chapter 4, we present our results on the triangular lattice in presence of anisotropy, focusing on two main regimes. In one case, the ground state is magnetically ordered, while in the other one there are evidences that backflow correlations favour a spin-liquid nature of the ground state, with one-dimensional features.
