Prof. Doutor Ricardo G. Dias
Departamento de Física - Universidade de Aveiro​

Abstract: Geometrically frustrated itinerant electronic systems exhibit flat bands in the energy dispersion, reflecting the existence of compact localized states. In this talk, we discuss some of the results of our recent research in these systems, namely: 
1. A set of rules for the construction of exact localized many-body eigenstates of the Hubbard model in decorated lattices, both for U=0 and U→∞. Using this simple set of rules, a tight-binding localized state in a plaquette can be divided, folded and unfolded to new plaquette geometries. This set of rules is also valid for the construction of a localized state for one hole in the U→∞ limit of the same plaquette, assuming a spin configuration which is a uniform linear combination of all possible permutations of the set of spins in the plaquette;
2. The two-terminal electronic conductance through the AB2 ring which is an simple example of the family of itinerant geometrically frustrated electronic systems. For zero magnetic flux, localized states in this system act as a filter of the zero frequency conductance peak, while for finite flux, the conductance exhibits a zero frequency peak with a dip which is a distinct fingerprint of the variable extension of the localized states.​