Real-space Renormalization Techniques Research Articles

Electronic states in zigzag carbon nanotube quantum dots

Local electronic properties of quantum dot nanotubes modeled by connecting pure semiconducting and metallic nanotubes via appropriate junctions are studied following a single $\ensuremath{\pi}$-band tight-binding Hamiltonian. The junctions are formed by introducing pair defects composed of heptagons and pentagons along the axial direction of pure nanotubes. We investigate the dependence of the confined electronic states with the characteristic sizes of the quantum dots taking into account different nanotube-based heterostructures. Quantum-well-like and interface states are characterized by investigating the spatial dependence of the local density of states of the discrete levels. We follow the Green's function formalism and adopt real-space renormalization techniques to calculate local density of states. The conductance of metal/semiconductor(metal)/metal carbon heterostructures is also investigated and we found exponentially the decay and oscillatory behaviors that may be associated with the electronic structure of the tube constituents and the details of the junctions.

Topology effects on local electronic properties and on the conductance of molecular structures

Electronic and transport properties of a class of low-dimensional systems are investigated within the Green-function formalism by adopting general real-space renormalization techniques. The effects of the lattice topology (coordination, dimension and structure) on the local density of states are discussed, mainly for energies close to the Fermi energy. An effective band gap is inferred by conductance calculations of molecular hybrid systems composed of a molecular wire and carbon nanotubes using the latter as metallic leads. An oscillatory behavior is found as a function of the interface number of links. Such theoretical analysis may certainly be useful for designing devices based on low-dimensional networks.

Statistical Physics: Statics, Dynamics, and Renormalization

Fundamentals of statistical physics: the lectures - a survey one particle and many Gaussian distributions quantum mechanics and lattices. Random dynamics: diffusion and hopping from hops to statistical mechanics correlations and response. More statistical mechanics: statistical thermodynamics Fermi, Bose, and other. Phase transitions: overview of phase transitions mean field theory of critical behaviour continuous phase transitions renormalization in one dimension real space renormalization techniques duality planar model and Coulomb systems XY model, renormalization and duality.

Metal–non-metal transition and specific heat of Kondo insulators

We study the metal–non-metal transition in Kondo insulators such as (Ce x La 1− x ) 3Bi 4Pt 3 as a function of x, magnetic field, pressure and temperature. The many body effects are treated diagonalizing the site Hamiltonian and embedding this solution into the lattice. The disorder is studied using a real space renormalization technique. The metal–insulator transition produced by the incorporation of La impurities is explained by the appearance of a delocalized level inside the conduction band.

One-dimensional contact process: Duality and renormalization

We study the one-dimensional contact process in its quantum version using a recently proposed real-space renormalization technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates that are comparable in accuracy with the best known in the literature.

Themetal-non-metal transition and specific heat of Kondo insulators

The metal-non-metal transition in Kondo insulators of the type(Ce1-xLax)3Bi4Pt3 is studied as a function of theLa (Kondo hole) concentration x. We explore the transition undervariation of the applied magnetic field, the pressure, and thetemperature. The many-body effects are treated by diagonalizing thesite Hamiltonian and embedding this solution into the lattice, usingthe chain approximation. The alloy states at the Fermi energy areobtained using a real-space renormalization technique. Themetal-insulator transition produced by the incorporation of Laimpurities is explained by the appearance of a delocalized levelinside the conduction band rather than by the creation of animpurity band at the gap.

S-matrix network models for coherent waves in random media: construction and renormalization

Networks of random quantum scatterers (S-matrices) form paradigmatic models for the propagation of coherent waves in random S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S-matrix network, hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the flow of the forward scattering strength ('conductance') under increasing system size. With the aid of 'small scale' numerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.

S‐matrix network models for coherent waves in random media: construction and renormalization

AbstractNetworks of random quantum scatterers (S‐matrices) form paradigmatic models for the propagation of coherent waves in random media. S‐matrix network models cover universal localization‐delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S‐matrix network, hierarchical network models can be constructed by recursion. The localization‐delocalization properties are contained in the flow of the forward scattering strength (‘conductance’) under increasing system size. With the aid of ‘small scale’ numerics qualitative aspects of the localization‐delocalization properties of S‐matrix network models can be worked out.

Real-space renormalization of the Chalker-Coddington model

We study a number of hierarchical network models related to the Chalker-Coddington model of quantum percolation. Our aim is to describe the physics of the quantum Hall transition. The hierarchical network models are constructed by combining series and parallel composition of quantum resistors. The localization-delocalization transition occurring in these models is treated by real-space renormalization techniques. Essentially, the localization-delocalization transition is due to a competition between two one-dimensional localization mechanisms.

Correlation functions of the 2D sine-Gordon model

A number of two-dimensional(2D) critical phenomena can be described in terms of the 2D sine-Gordon model. With the bosonization, several 1D quantum systems are also transformed to the same model. However, the transition of the 2D sine-Gordon model, Berezinskii-Kosterlitz-Thouless(BKT) transition, is essentially different from the second-order transition. The divergence of the correlation length is more rapid than any power-law, and there are logarithmic corrections. These pathological features make difficult to determine the BKT transition point and critical indices from finite-size calculations. In this paper, we calculate the several correlation functions of this model using a real-space renormalization technique. It is found that the several correlation functions, or eigenvalues of the corresponding transfer matrix for a finite system, become degenerate on the BKT line including logarithmic corrections. By the use of this degeneracy, which reflects the hidden SU(2) symmetry on the BKT line,it is possible to determine the BKT critical line with high precision from small size data, and to identify the universality class. In addition, a new universal relation is found. This reveals the relation between the Abelian and the non-Abelian bosonization.

SCALING OF RESISTANCE IN THE TWO-DIMENSIONAL ANDERSON TIGHT-BINDING MODEL OF DISORDERED SYSTEMS II

Several workers using different numerical methods have in recent times obtained algebraic decay of wave function amplitudes for localized states at the band center of a two-dimensional disordered system. These include vector recursion,1 direct diagonalization,2 and real space renormalization techniques.3 We modify a version of the combined real space renormalization and vector recursion techniques, including the effect of the random environment on the phase differences between the electronic incoming waves through the different incoming leads, to confirm the algebraic or weak localization at the band center of a random tight-binding Anderson model in two dimensions.

Interband resonant tunneling and transport in InAs/AlSb/GaSb heterostructures.

The nonequilibrium Green-function Keldysh formalism is used to analyze resonant interband tunneling in double-barrier structures and nonresonant interband transport in polytype heterostructures of InAs, GaSb, and AlSb. The systems are modeled by a multiband tight-binding Hamiltonian that incorporates mixing of electron, light-hole, and heavy-hole states. The model is solved by the real-space renormalization technique, which is very rapid and numerically stable for any size of the system. The large difference in effective masses and the opposite curvature of the energy dispersion of the conduction band in InAs and valence bands in GaSb are reflected in the transport properties. The I-V characteristics of double-barrier structures show quite different features according to whether the well is InAs or GaSb. For the latter case, the current intensity peaks and the peak-to-valley current ratios are much larger than for the former case. The calculated I-V characteristics are generally in very good agreement with the experimental data. The density of states and the dispersion relation of the resonant states as a function of the in-plane wave vector are also discussed.

Correlated two-component percolation

A correlated two-component percolation model is constructed to treat random bonds between next-nearest neighbours. Monte Carlo simulations on a 2D square lattice are performed. By employing real-space renormalization techniques, it is proved that the criticality is controlled by a single fixed point and the percolation exponents are unaffected by correlations. The discovered power law dependence with exponent 1/v of the percolation threshold pc on the concentration of the second phase is discussed.

D.C. conductivity calculation and the percolation threshold in dilute Bethe lattices

Abstract The percolation threshold for a dilute Bethe lattice is determined applying real space renormalization techniques within the Green function formalism for the calculation of the d.c. electrical conductivity. The quantum percolation is attained for a higher concentration of present bonds than in the classical problem.

Application of real-space renormalization techniques to one-dimensional models.

Sarker's real-space renormalization-group method, applied previously to the one-dimensional dimerized XY model, is used to study the one-dimensional pure and dimerized Heisenberg models. Comparison of critical exponents (the dynamical and the gap exponents) with exact or conjectured values indicates that the method, in its original version, does not yield an improved real-space technique, at least for the models studied for which the opening of the gap leads to essential singularity or logarithmic corrections.

Real-space renormalization-group study of fractal Ising models.

Ising models on Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski carpets are studied within a real-space renormalization technique. A specific method for decimating spin blocks of any size is proposed as an alternative to the bond-moving prescription, and its accuracy is checked on various examples. From an analysis of the critical couplings we estimate some of the finite-size effects of Monte Carlo simulations of fractals. The exponent \ensuremath{\nu}, computed for a large variety of carpets, is found smaller than in the bond-moving approach but with the same behavior under variations of the fractal parameters. No universality criterion emerges except in the limit of vanishing lacunarity.

Selective renormalization in real space: A simple approach to intermediate-wavelength properties of granular structures

A new real-space renormalization technique is introduced, aimed at simplifying the computation of dynamical properties of granular structures at wavelengths of order a typical grain size. The technique consists in replacing the large number of atoms within a grain by a small number of rigid masses and choosing the couplings between the masses to reproduce the low-lying properties of the isolated grains. The transformation is shown to yield results that converge rapidly to the exact solution for the dynamical properties at intermediate wavelengths.

Vortex-ring model of the superfluid lambda transition.

An initial model of the superfluid \ensuremath{\lambda} transition is constructed with use of vortex-ring excitations, as originally suggested by Onsager and Feynman. A real-space renormalization technique generates a screened vortex energy and core size, and gives rise to a transition where rings of infinite diameter are excited as the superfluid density approaches zero at ${\mathrm{T}}_{\mathrm{c}}$. Although the model satisfies the Josephson hyperscaling relation, it is not yet a complete theory: The superfluid density exponent is \ensuremath{\nu}=0.53, and does not match the known value \ensuremath{\nu}=0.67.

Electronic Properties of Amorphous Semiconductors. Lattice Topology Effects

AbstractThe influence is studied of the lattice topology in the electronic properties of a tetrahedrally bonded amorphous semiconductor, typically a‐Si. The system is described by a nearest neighbour tight‐binding Hamiltonian, defined on a pseudolattice. The topology corresponding to the perfect gasket defined using hexagons as its basic structure is similar to the crystalline diamond lattice. The continuum random network is simulated by generating vacancies in the gasket lattice where dangling bonds are eliminated by saturation. The electronic density of states and the ring statistics of the disorder lattice are studied using a real space renormalization technique within the context of the Green function formalism.

Vortices and the Super fluid λ-Transition

An initial model of the superfluid λ-transition is constructed using vortex-ring excitations, as originally suggested by Onsager and Feynman. A real-space renormalization technique generates a screened vortex energy and core size, and gives rise to a transition where rings of infinite diameter are excited as the superfluid density approaches zero at Tc. Although the model satisfies the Josephson hyperscaling relation, it is not yet a complete theory: the superfluid density exponent is v=0.53, and does not match the known value v=0.67.