Banca de DEFESA: WILIAM DA SILVA OLIVEIRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE: WILIAM DA SILVA OLIVEIRA
DATA: 16/04/2021
HORA: 13:30
LOCAL: Remota - Plataforma Google Meet
TÍTULO: Percolação clássica e quântica na rede de Lieb
PALAVRAS-CHAVES: rede de Lieb 2D; rede de Lieb 3D; percolação clássica; percolação quântica; modelo tight-binding.
PÁGINAS: 37
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
RESUMO:

Magnetic systems have been extensively investigated over the last
few decades, in many cases modeled by random dilution of sites or bonds. The
dilution has the function of modeling the presence of non-magnetic impurities in
the system, allowing us to study their behavior as a function of the
concentration of diluted sites. In this context, the Lieb lattice has been
previously used to study several interesting physical phenomena such as
superconductivity and ferromagnetism. In light of this, in the present work we
studied classical site and bond percolation (2D and 3D) and quantum site
percolation (3D), on the Lieb lattice, with the objective of determining their
percolation thresholds pc (classic) and pq (quantum), which are still unavailable
in the literature. To study the classical case we used the Hoshen-Kopelman
algorithm to identify the percolating cluster and finite size scaling to determine

the critical percolation threshold and the exponent ν at the thermodynamic limit.
In the quantum case we analyzed the energy level’s statistics through Random
Matrix Theory, considering a tight-binding hamiltonian. For the purpose of
calibrating the methods described here, we determine the critical thresholds and
exponents ν for classical site and bond percolation in square and simple cubic
lattices and quantum site percolation in a simple cubic lattice. Investigating the
classical site percolation for the 2D Lieb lattice, we found the critical threshold
pc = 0.7384 ± 0.0004 and ν = 1.3 ± 0.04, and for bond percolation we obtained
pc = 0.6438 ± 0.0003 and ν = 1.29 ± 0.02. In three dimensions, the Lieb lattice
was modeled in two ways defined here as Lieb lattice without decoration and
with decoration. For the Lieb lattice without decoration, the value of the critical
threshold of site percolation and critical exponent found were pc = 0.3919 ±
0.0006 and ν = 0.86 ± 0.05, respectively. In this same lattice, for bond
percolation we found pc = 0.3345 ± 0.0005 and ν = 0.95 ± 0.04. For the
decorated lattice, employing site percolation, we obtained pc = 0.5225 ± 0.0005
and ν = 0.89 ± 0.04 and, in this same lattice for bond percolation, we found pc =
0.4014 ± 0.0006 and ν = 0.93 ± 0.05. Researching quantum site percolation on
the Lieb lattice without decoration and considering only three dimensions, we
found pq = 0.552 ± 0.01 and ν = 1.65 ± 0.05 and, for the Lieb lattice with
decoration we obtained pq = 0.710±0.01 and ν = 1.44 ± 0.05. The ν exponent
for classical percolation in the 2D and 3D Lieb lattice are consistent with the
universality class of classical percolation in the square and simple cubic lattices,
respectively, according to the existing literature. This is also verified when we
compare the exponent ν for the quantum site percolation case in 3D lattices,
with results available in the literature regarding quantum site percolation in
simple cubic lattice. The methodology used here, to examine classical and
quantum percolation, has been proved effective to obtain coherent results.

MEMBROS DA BANCA:
Interno - 1446938 - FRANCISCO WELINGTON DE SOUSA LIMA
Presidente - 423297 - JOSE PIMENTEL DE LIMA
Externo ao Programa - 010.453.033-21 - NATANAEL DE CARVALHO COSTA - UFRJ
Externo ao Programa - 344.235.407-20 - RAIMUNDO ROCHA DOS SANTOS - UFRJ