Quantum percolation on Lieb Lattices W. S. Oliveira, J. Pimentel de Lima, Raimundo R. dos Santos Physical Review E, 2025 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.
Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker Sebastião dos Anjos Sousa-Júnior, Marcus V. de S. Ferraz, José P. de Lima, Tarik P. Cysne Physical Review B, 2025 In this work, we use the local spin Chern marker (LSCM) recently introduced by Ba\`u and Marrazzo [Phys. Rev. B 110, 054203 (2024)] to analyze the real-space ($\mathbf{r}$-space) topology of the ground-state electronic wave functions in a honeycomb structure described by three distinct models. The models considered here are characterized by strong Rashba spin-orbit interaction, which leads to nonconservation of the spin operator, i.e., $[\mathcal{H},{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{s}}_{z}]\ensuremath{\ne}0$. The three spin-orbit couplings associated with the topological aspects of the models are as follows: (1) standard Kane-Mele coupling, (2) sublattice-dependent Kane-Mele coupling, and (3) in-plane (${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{s}}_{y}$) polarized Kane-Mele coupling. These couplings occur in graphene grown on suitable substrates and are relevant for modeling its van der Waals heterostructures. A particular topological phase diagram characterizes each of these spin-orbit interactions, and our calculations of LSCM, fully performed on $\mathbf{r}$ space, successfully capture its general features. We also performed a detailed analysis of the spectral properties of the energy and valence-projected spin-matrix eigenvalues, which shows that both exhibit a gap that protects the marker. To complement, we examine the effect of disorder and spatial inhomogeneities on the LSCM for the different lattice models addressed in our work. Our results expand the applicability of the spin Chern number method to a class of lattice Hamiltonians with experimental relevance and may contribute to future research on the real-space topology of realistic materials.
Two-dimensional t-t′ Holstein model Maykon V. Araújo, José P. de Lima, Sandro Sorella, Natanael C. Costa Physical Review B, 2022 The competition and interplay between charge-density wave and superconductivity have become a central subject for quasi-two-dimensional compounds. Some of these materials, such as the transition-metal dichalcogenides, exhibit strong electron-phonon coupling, an interaction that may favor both phases, depending on the external parameters, such as hydrostatic pressure. In view of this, here we analyze the single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Holstein model in the square lattice, adding a next-nearest neighbor hopping ${t}^{\ensuremath{'}}$ in order to play the role of the external pressure. To this end, we perform unbiased quantum Monte Carlo simulations with an efficient inversion sampling technique appropriately devised for this model. Such a methodology drastically reduces the autocorrelation time and increases the efficiency of the Monte Carlo approach. By investigating the charge-charge correlation functions, we obtain the behavior of the critical temperature as a function of ${t}^{\ensuremath{'}}$ and, from compressibility analysis, we show that a first-order metal-to-insulator phase transition occurs. We also provide a low-temperature phase diagram for the model.
Percolation on Lieb lattices W. S. Oliveira, J. Pimentel de Lima, N. C. Costa, R. R. dos Santos Physical Review E, 2021 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 or to a perovskite lattice. 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 LLs 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.
Superconducting Kondo phase in an orbitally separated bilayer Sebastião dos Anjos Sousa-Júnior, José P. de Lima, Natanael C. Costa, Raimundo R. dos Santos Physical Review Research, 2020 The authors find that proximity effects of an additional metallic/superconducting layer close to a Kondo-lattice modify the collective transport properties relative to separate layers. The Kondo-insulator state is suppressed, and a superconducting Kondo phase sets in, with the occurrence of unconventional pairing amplitudes involving f-electrons
Dynamical resilience to disorder: The dilute Hubbard model on the Lieb lattice L. Oliveira-Lima, N. C. Costa, J. Pimentel de Lima, R. T. Scalettar, R. R. dos Santos Physical Review B, 2020 In itinerant systems, electron-electron interactions may lead to the formation of local magnetic moments and their effective exchange coupling, which in turn gives rise to long-range magnetic order. Therefore, when moment formation is weakened, such as in the single-band Hubbard model on a square lattice with the on-site repulsion being randomly switched off on a fraction $x$ of sites, magnetic order is suppressed beyond some critical ${x}_{c}$, which was found to lie below the classical percolation threshold ${x}_{c}^{\text{(perc,sq)}}$. Here we study dilute magnetism in flat band systems, namely, in the Hubbard model on a ``Lieb'' lattice. Interestingly, we show that magnetic order persists to $x$ almost twice as large as the classical percolation threshold for the lattice, thus emphasizing the central role of electron itinerancy to the magnetic response. The analysis of the orbital-resolved order parameters reveals that the contribution of the fourfold coordinated ``$d$'' sites to magnetism is dramatically affected by dilution, while the localized ``$p$'' states of the flat band provide the dominant contribution to long-range correlations. We also examine the transport properties, which suggest the existence of an insulator-to-metal transition in the same range of the critical magnetic dilution.
Study of spatial correlations in a crumpled wire trapped in two-dimensional cavities of different topologies José Pimentel de Lima, Fábio Nascimento de Sousa, Valdemiro da Paz Brito, Marcelo Andrade de Filgueiras Gomes Physica Scripta, 2020 Abstract In this paper, it is reported a study of spatial correlations in configurations of a plastic wire trapped in two-dimensional planar cavities of different topologies defined by particular distributions of fixed pins that introduce excluded domains. The configurations examined were obtained from an extensive experimental study that shows that the jammed packing fraction of the wire within the cavities depends heavily on the topology of the cavity. The analysis reveals regions of the configurations dominated by finite-size effects controlled by the drive force of injection, and bulk domains strongly controlled by the density of pins. In the bulk regime a persistence length, as obtained in the Kratky–Porod model of polymers, is found to depend linearly with the number of pins which develops the role of an inverse effective temperature. That is, the temperature for the system in this case depends on the topology of the space. The regions characterized by finite-size effects present two regimes corresponding to different mechanical rigidities.
A mean-field approach to Kondo-attractive-Hubbard model Natanael C Costa, José P de Lima, Thereza Paiva, Mohammed El Massalami, Raimundo R dos Santos Journal of Physics Condensed Matter, 2018 Abstract With the purpose of investigating coexistence between magnetic order and superconductivity, we consider a model in which conduction electrons interact with each other, via an attractive Hubbard on-site coupling U , and with local moments on every site, via a Kondo-like coupling, J . The model is solved on a simple cubic lattice through a Hartree–Fock approximation, within a ‘semi-classical’ framework which allows spiral magnetic modes to be stabilized. For a fixed electronic density, n c , the small J region of the ground state ( T = 0) phase diagram displays spiral antiferromagnetic (SAFM) states for small U . Upon increasing U , a state with coexistence between superconductivity (SC) and SAFM sets in; further increase in U turns the spiral mode into a Néel antiferromagnet. The large J region is a (singlet) Kondo phase. At finite temperatures, and in the region of coexistence, thermal fluctuations suppress the different ordered phases in succession: the SAFM phase at lower temperatures and SC at higher temperatures; also, reentrant behaviour is found to be induced by temperature. Our results provide a qualitative description of the competition between local moment magnetism and superconductivity in the borocarbides family.
