arXiv subjects

W. S. Oliveira

Publications and source records attributed to W. S. Oliveira.

6 recordsLinked to original sources

arXiv2026

Enhanced Multifractality Induced by Non-Hermitian Disorder in Quantum Percolation

We investigate the interplay between geometric dilution and non-Hermitian disorder in the two-dimensional quantum site-percolation model. Non-Hermiticity is introduced through random imaginary on-site potentials, representing spatially uncorrelated gain and loss, while the hopping amplitudes remain reciprocal. By combining complex level-spacing statistics, participation entropy, and multifractal analysis, we characterize the localization properties of the eigenstates as functions of the disorder and the non-Hermiticity strength. Our finite-size scaling results show that non-Hermitian disorder shifts the quantum percolation threshold ($p_q$) toward larger occupation probabilities. Consequently, the fully delocalized phase is progressively suppressed and disappears at sufficiently strong disorder. This suppression is not a simple consequence of adding on-site disorder of a given strength, but is specifically enhanced by its imaginary character, as an equally strong real (Hermitian) on-site potential produces a weaker shift of $p_q$. Nevertheless, the intermediate region between the classical ($p_c$) and quantum percolation thresholds presents a genuine multifractal critical phase, while the localization-length exponent $ν$ remains the same, relative to its Hermitian value. Altogether, our results demonstrate that random gain and loss enhance the multifractal regime while preserving the universality class of the quantum percolation transition.

cond-mat.dis-nn↗

arXiv2026

Quantum percolation in honeycomb lattices under random spin-orbit coupling

We investigate quantum percolation in a honeycomb lattice with site dilution and random spin-orbit coupling. Using exact diagonalization combined with finite-size scaling analysis, we study the metal-insulator transition, extracting the quantum percolation threshold $p_q$, and the correlation-length exponent, $ν$. In the absence of spin-orbit coupling, we find that $p_q$ remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold $p_c$ of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling, $p_q$ tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.

cond-mat.dis-nn↗

arXiv2025

Berezinskii-Kosterlitz-Thouless Transition and Multifractal Critical Phase in Two-Dimensional Quantum Percolation

We present a numerical study of the two-dimensional quantum percolation model, revealing that a critical region with multifractal eigenstates mediates the transition from localized to delocalized states. By analyzing the mean level ratio and participation entropy, we identify two distinct transitions: a Berezinskii-Kosterlitz-Thouless (BKT) transition at the classical percolation threshold, separating the localized and critical phases, and a power-law-type transition at a larger concentration, marking the onset of full delocalization. The critical phase is characterized by multifractal eigenstates, as evidenced by the generalized fractal dimension and multifractal spectrum. Altogether, our results establish that in the marginal two-dimensional case, the Anderson impurity model and the quantum percolation model belong to different universality classes.

cond-mat.dis-nn↗

arXiv2024

Quantum percolation on Lieb Lattices

We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with $ν$ decreasing with lattice dimensionality, $d$, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.

cond-mat.stat-mech↗

arXiv2021

Percolation on Lieb lattices

We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO$_2$ lattice; in three dimensions it can be generalized to a layered Lieb lattice (LLL) or to a perovskite lattice (PL). Emergent electronic phenomena, such as topological states and ferrimagnetism, have been predicted to occur in these systems, which may be realized in optical lattices as well as in solid state. Since the study of the interplay between quantum fluctuations and disorder in these systems requires the availability of accurate estimates of geometrical critical parameters, such as percolation thresholds and correlation length exponents, here we use Monte Carlo simulations to obtain these data for Lieb lattices when a site (or bond) is present with probability $p$. We have found that the thresholds satisfy a mean-field (Bethe lattice) trend, namely that the critical concentration, $p_c$, increases as the average coordination number decreases; our estimates for the correlation length exponent are in line with the expectation that there is no change in the universality class.

cond-mat.stat-mech↗

arXiv2014

Mott-Anderson transition in disordered charge transfer model: insights from typical medium theory

The Mott-Anderson transition in the disordered charge-transfer model displays several new features in comparison to what is found in the disordered single-band Hubbard model, as recently demonstrated by large-scale computational (statistical dynamical mean field theory) studies. Here we show that a much simpler typical medium theory approach (TMT-DMFT) to the same model is able to capture most qualitative and even quantitative aspects of the phase diagram, the emergence of an intermediate electronic Griffiths phase, and the critical behavior close to the metal-insulator transition. Conceptual and mathematical simplicity of the TMT-DMFT formulation thus makes it possible to gain useful new insight into the mechanism of the Mott-Anderson transition in these models.

cond-mat.str-el↗