Description
Many interesting physical phenomena are connected to strongly correlated systems, which, due to their complexity, cannot usually be studied analitically, making numerical approaches essential. The development of the latter and the study of the physical scenarios induced by strong correlations are therefore both of great importance. In this context, I will present the results of my numerical investigations of strongly correlated systems: specifically, i) the ground-state phase diagram of a bosonic cluster-forming model of interest for cold atom experiments, as well as ii) the ground-state properties of the fermionic t-J model, a candidate Hamiltonian to describe high-T_c superconductivity, in the presence of two mobile holes. Path Integral and Variational Monte Carlo have been chosen as numerical techniques for the two problems, respectively. The main results I will discuss are the demonstration of a ground-state supersolid-supersolid transition in the bosonic scenario, and of a d-wave hole bound state in the fermionic model. My investigation of the latter in the 2-hole case is foundational for the application of my approach of choice to other problems, of direct interest for high-T_c superconductivity, where the physical picture is still unclear (such as thecase of finite hole concentration).
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