Modelo de Hubbard bidimensional: rede hexagonal desordenada e ...

Abstract
Two-dimensional Hubbard model:
Disordered Honeycomb Lattice and Square Lattice With Superlattices
Rubem Mondaini
Advisor: Thereza Cristina Lacerda Paiva
Abstract of Thesis presented to Programa de Pós-graduação em Física do Instituto de Física da Uni-
versidade Federal do Rio de Janeiro, as a partial fulfillment of the requirements for the degree of Master of
Science – M.Sc. – (Physics).
We study two kinds of two-dimensional systems: structured (superlattices in the square
lattice) and disordered (honeycomb lattice), both in the approach of strongly correlated
fermions. For this, we adopt the Hubbard model in the grand-canonical ensemble with
the necessary generalizations to simulate each one of these systems. We use the Deter-
minantal Quantum Monte Carlo as the numerical method to obtain the desired physical
quantities. In the superlattice system we set the local electronic interaction U = 0 in cer-
tain layers with the purpose to simulate the non-magnetic layers. The magnetic layers are
simulated by considering U = 0. We obtain the behavior of the magnetic ordering as well
as the transport properties like the dc conductivity for the half-filled band and away from
this filling. We also compare the two most used approaches of the Hamiltonian of the
problem. We were able to determine the critical ratio of the number of repulsive layers to
the free ones that separate the insulating and metallic behaviors. In the honeycomb lattice
we simulate the effect of disorder in the local energy levels of each site and observe how