Low density ferrromagnetism in a square-to-triangular lattice

This thesis investigates the emergence of ferromagnetism in two-dimensional Hubbard models on geometrically frustrated lattices, focusing on the continuous transition from square to triangular geometries. The motivation comes from recent progress in ultracold atom experiments, where lattice geometry can be tuned with high precision, opening new possibilities to study frustration-driven quantum magnetism. We employ the T-matrix approximation to analyze the competition between kinetic energy, interaction strength, and lattice frustration at low particle densities. By extending the T-matrix framework to both finite lattices and the thermodynamic limit, we perform accurate energy comparisons between paramagnetic and ferromagnetic states. Our results yield phase diagrams that map out the conditions for the stabilization of ferromagnetism as frustration is varied, providing theoretical guidance for experiments with ultracold optical lattices and offering new insights into the microscopic mechanisms of itinerant ferromagnetism.