Random On-site Energies Research Articles

Effect of random on-site energies on the critical temperature of a lattice Bose gas

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν 20 . By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν 20 ≪ 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.

Interplay between interaction and (un)correlated disorder in one-dimensional many-particle systems: delocalization and global entanglement

We consider a one-dimensional (1D) quantum many-body system and investigate how the interplay between interaction and on-site disorder affects spatial localization and quantum correlations. The hopping amplitude is kept constant. To measure localization, we use the number of principal components (NPC), which quantifies the spreading of the system eigenstates over vectors of a given basis set. Quantum correlations are determined by a global entanglement measure Q, which quantifies the degree of entanglement of multipartite pure states. Our studies apply analogously to a 1D system of interacting spinless fermions, hard-core bosons, or yet to an XXZ Heisenberg spin-1/2 chain. Disorder is characterized by both uncorrelated and long-range correlated random on-site energies. Dilute and half-filled chains are analyzed. In half-filled clean chains, delocalization is maximum when the particles do not interact, whereas multi-partite entanglement is largest when they do. In the presence of uncorrelated disorder, NPC and Q show a nontrivial behavior with interaction, peaking in the chaotic region. The inclusion of correlated disorder may further extend two-particle states, but the effect decreases with the number of particles and the strength of their interactions. In half-filled chains with large interaction, correlated disorder may even enhance localization.

Von Neumann entropy and on-site localization for perpetually coupled qubits

We use the von Neumann entropy to study the single- and many-particle on-site localizations of stationary states for an anisotropic Heisenberg spin-$\frac{1}{2}$ chain. With a constructed bounded sequence of on-site energies for single- and many-particle systems we demonstrate that the von Neumann entropy approaches zero, indicating strong on-site localizations for all states. On the contrary, random on-site energy sequence does not lead to strong on-site confinement of all states. Our numerical results indicate that the von Neumann entropy provides insight to analyze on-site localizations for these systems.

Localization properties of a tight-binding electronic model on the Apollonian network

An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex network and as a substrate on the top of which physical models can be defined. The Schr\"odinger equation of the model, which includes only nearest-neighbor interactions, is written in a matrix formulation. In the uniform case, the resulting Hamiltonian is proportional to the adjacency matrix of the Apollonian network. The characterization of the electronic eigenstates is based on the properties of the spectrum, which is characterized by a very large degeneracy. The $2\ensuremath{\pi}/3$ rotation symmetry of the network and large number of equivalent sites are reflected in all eigenstates, which are classified according to their parity. Extended and localized states are identified by evaluating the participation rate. Results for other two nonuniform models on the Apollonian network are also presented. In one case, interaction is considered to be dependent of the node degree, while in the other one random on-site energies are considered.

Investigation of gas sensing properties of armchair graphene nanoribbons

A theoretical approach based on a tight-binding model is developed for studying theeffects of finite concentration gas adsorption (for what are known as diatomic,triatomic and quadratomic gas molecules in the general forms denoted byXY,XY2 and XY3, respectively) on electronic properties of armchair graphene nanoribbons (AGNRs). Toconsider the edge effects on electronic properties of pure AGNRs for the firsttime, two hopping parameters, for hydrogen–carbon and carbon–carbon nearestneighbor hopping, are considered. We found, for some specified values of hoppingintegrals and random on-site energies, that adsorbed molecule AGNRs act asdonors or acceptors, which is consistent with reported experimental results for CO,NO2,O2,N2,CO2 and NH3 adsorption on graphene. Then by using these parameters and the coherent potentialapproximation, we investigated the effect of finite concentration gas molecule adsorption onthe average density of states. Our results could be used to make p-type or n-typesemiconductors by means of finite concentration adsorption of gas molecules or a gassensor.

Ultracold bosons in lattices with binary disorder

Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.

Static screening and delocalization effects in the Hubbard-Anderson model

We study the suppression of electron localization due to the screening of disorder in a Hubbard-Anderson model. We focus on the change of the electron localization length at the Fermi level within a static picture, where interactions are absorbed into the redefinition of the random on-site energies. Two different approximations are presented, either one yielding a nonmonotonic dependence of the localization length on the interaction strength, with a pronounced maximum at an intermediate interaction strength. In spite of its simplicity, our approach is in good agreement with recent numerical results.

Finite-concentration gas molecule adsorption on carbon nanotubes investigated by a tight-binding approach

A theoretical approach based on tight-binding model is developed to study the effects of finite concentrations of adsorption of diatomic gas molecules (in the general form denoted by ${X}_{2}$) and also triatomic gas molecules (in the general form denoted by $Y{X}_{2}$) on the single-walled carbon nanotube (SWCNT) electronic properties. To obtain proper hopping integrals and random on-site energies, for the case of one molecule adsorption, the local density of states for various hopping integrals and random on-site energies are calculated. We found, for some specified values of hopping integrals and random on-site energies, adsorbed molecule bound states located inside the (10,0) SWCNT energy gap, where it is consistent with the reported experimental results for ${\mathrm{O}}_{2}$ and $\mathrm{N}{\mathrm{O}}_{2}$ adsorption, while for other values, there are no bound states inside of energy gap. The last case is similar to the ${\mathrm{N}}_{2}$ and $\mathrm{C}{\mathrm{O}}_{2}$ adsorption on semiconductor SWCNTs. Then, by using these obtained parameters and coherent potential approximation, we investigate the effects of finite gas molecule adsorption on the average density of states. Our results could be used to make a $p$-type or $n$-type semiconductors by finite-concentration adsorption of gas molecules.

LYAPUNOV EXPONENT AND THE LOCALIZED PROPERTIES OF ELECTRONIC STATES OF ONE-DIMENSIONAL DISORDERED BINARY ALLOY

Based on the tight-binding model of the single electron, the one-dimensional Anderson model with random binary distributed on-site energies is studied using the transfer-matrix approach. We calculate numerically the localization length, the density of the electronic states and the Lyapunov exponent. The results show that the localization length strongly depends on energies and is affected by disordered degrees to some extent. With finite size systems, the localization length presents obvious effect on the impurity concentration. While in the dilute limit there exist extended states, increasing the impurity concentration beyond a critical value destroys these extended states and the localization length over the entire energy range becomes smaller than the system size. By studying the scaling relation, we find that the localized states are stable in the thermodynamic limit. Transforming the random matrix product into a conformal map, we introduce the Lyapunov exponent, which is finite within the entire band in our model. Starting from the Lyapunov exponent, the localization length and the density of states may also be obtained.

Electronic properties of disordered corner-sharing tetrahedral lattices

We have examined the behaviour of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width W, of random on-site energies. We have used both the relative localization length and the spectral rigidity to analyze the nature of the eigenstates, and have determined both the mobility edge trajectories as a function of W, and the critical disorder, Wc, beyond which all states are localized. We find (i) that the mobility edge trajectories (energies Ec vs. disorder W) are qualitatively different from those found for a simple cubic lattice, and (ii) that the spectral rigidity is scale invariant at Wc and thus provides a reliable method of estimating this quantity -- we find Wc/t=14.5. We discuss our results in the context of the metal-to-insulator transition undergone by LiAlyTi{2-y}O4 in a quantum site percolation model that also includes the above-mentioned Anderson disorder, and show that the effects produced by Anderson disorder are far less important than those produced by quantum site percolation, at least in the determination of the doping concentration at which the metal-to-insulator transition is predicted to occur.

Universal parameter at the Anderson transition on a one-dimensional lattice with non-random long-range coupling

We study numerically the localization–delocalization transition in a class of one-dimensional tight-binding Hamiltonians H with non-random power-law inter-site coupling H mn=J/|m−n| μ and random on-site energy. This model is critical with respect to the magnitude of disorder at one of the band edges, provided 1<μ< 3 2 . We demonstrate that at some value of the magnitude of disorder Δ c, interpreted as the critical one, the ratio of the standard deviation to the mean of the participation number distribution is a size-invariant parameter: all curves of this ratio versus the magnitude of disorder, plotted for different system sizes, have a joint intersection point at Δ c. This value is finite for 1<μ< 3 2 implying the existence of the transition, while in the marginal case (at μ= 3 2 ) the intersection point is at Δ c=0 implying localization of all the eigenstates.

Effects of diagonal disorder on charge density wave and superconductivity in local pair systems

We analyse the influence of diagonal disorder (random site energy) on charge density wave (CDW) and superconductivity (SS) in local pair systems which are described by the model of hard core charged bosons on a lattice. This problem was previously studied within the mean field approximation for the case of half-filled band ( n=1). Here we extend that investigation to the case of arbitrary particle concentration (0< n<2) and examine the phase diagrams of the model and the behaviour of superfluid density ( ρ s) as a function of n and the increasing disorder. Depending on the strength of random on-site energies, the intersite density–density repulsion and the concentration, the model can exhibit several various phases, including homogeneous phases: CDW, SS and Bose-glass (NO) as well as the phase separated states: CDW–SS, CDW–NO and particle droplets. The obtained results for SS phase are in qualitative agreement with the available Monte-Carlo calculations for two-dimensional lattice. Also, in a definite range of parameters, the system exhibits the phenomena which we call a disorder induced superconductivity and a disorder induced charge ordering.

Spectral and transport properties of strongly correlated disordered systems

It is shown that strong electron-electron interactions in disordered systems lead to the enhancement of intrinsic disorder. The one-band Hubbard model with random on-site energies is studied in the infinite U limit. Electron correlations are treated in the mean-field slave boson technique. To average over disorder, both intrinsic (diagonal) and interaction induced (off-diagonal), we use a version of the coherent potential approximation. We illustrate the approach by calculating density of states, ac electrical conductivity, and effective carrier concentration. The obtained results are discussed in the context of recent experimental data on disordered strongly correlated materials.

Correlation-induced metal-insulator transition in the one-dimensional Anderson model

We study the nature of the electronic states in tight-binding one-dimensional models with long-range correlated disorder. In particular, we study both diagonal and off-diagonal chains. The energies are considered to be in such a sequency to describe the trace of a fractional Brownian motion with a specified spectral density S( k)∝1/ k α . Using a renormalization group technique, we show that for random on-site energy sequences with anti-persistent increments ( α<2) all energy eigenstates are exponentially localized. On the other hand, for on-site energy sequences with persistent increments ( α>2), the Lyapunov coefficient (inverse localization length) vanishes within a finite range of energy values revealing the presence of an Anderson-like metal–insulator transition. In the case of off-diagonal disorder a phase of delocalized states becomes stable for any α>1.

On the Interplay of Disorder and Correlations

I address here the question of the mutual interplay of strong correlations and disorder in the system. I consider random version of the Hubbard model. Diagonal randomness is introduced via random on-site energies and treated by the coherent potential approximation. Strong, short ranged, electron - electron interactions are described by the slave boson technique and found to induce additional disorder in the system. As an example I calculate the density of states of the random interacting binary alloy and compare it with that for non-interacting system.

Numerical simulations for superconductors with strong randomness

The Bogoliubov-de Gennes equation including random on-site energy is solved on a N × N square-lattice for both s- and d x 2− y 2 -wave superconductors, using a numerical diagonalization technique. The density of states and the distribution of the gap parameters are presented for various intensities of the random potential.

Phase diagram of disordered boson systems in the presence of random hopping.

We consider a generalization of the hard-core disordered boson system with the inclusion of random boson hopping. The phase diagrams are obtained, and the effects of the random boson hopping on the zero-temperature quantum phase transitions are studied. The existence of Bose-glass and superfluid glass phases is also investigated. The behavior of both continuous and first-order transitions as well as the tricritical point is discussed as a function of the strength of random on-site energies. The possible Bose glass displayed by the system due to the presence of the disorder is examined. \textcopyright{} 1996 The American Physical Society.

Field theoretic treatment of the strong-coupling attractive Hubbard model with diagonal disorder

The authors present a field theoretic formulation of the strong-coupling attractive Hubbard model with Gaussian distributed random on-site energies. Self-consistency equations for the order parameters of superconductivity and charge ordering are derived at lowest loop order and solved for the limiting cases of weak and strong disorder. They also study dynamical properties and calculate the influence of disorder on the Bogoliubov-Anderson mode in the superconducting phase.

Renormalization-group study of the Anderson-Hubbard model

We study the half-filled Hubbard model with random on-site energies with the use of a real-space renormalization group. For $d=1$, we find a transition from an Anderson insulator to a Hubbard insulator as the Hubbard $U$ is increased. We find no metallic phase. For $d=3$, we find a metallic phase which, surprisingly, is stabilized against Anderson localization by a small Hubbard $U$.