This PhD project concerns the theoretical study of doped Mott insulators on geometrically frustrated lattices, where strong correlations, magnetism, and lattice geometry are closely linked. In these systems, doping does not simply restore conventional metallic behavior but can instead generate competing tendencies toward magnetic order, valence-bond correlations, and other collective quantum states, such as superconductivity. Previous work has shown that interference and flat-band effects can suppress standard ferromagnetic mechanisms on frustrated lattices, while more recent developments suggest that carrier motion itself can promote new correlated phases.

 

The project will investigate which microscopic mechanisms govern this evolution upon doping. The main goals are to determine how kinetic frustration, band structure, and interactions influence the stability of ordered and nontrivial quantum phases, and to establish a more systematic picture across triangular, kagome, pyrochlore, and related lattices, including altermagnets.