arXiv subjects

Michael Schreiber

Publications and source records attributed to Michael Schreiber.

At least 145 records · Page 8Linked to original sources

arXiv1998

Differences between regular and random order of updates in damage spreading simulations

We investigate the spreading of damage in the three-dimensional Ising model by means of large-scale Monte-Carlo simulations. Within the Glauber dynamics we use different rules for the order in which the sites are updated. We find that the stationary damage values and the spreading temperature are different for different update order. In particular, random update order leads to larger damage and a lower spreading temperature than regular order. Consequently, damage spreading in the Ising model is non-universal not only with respect to different update algorithms (e.g. Glauber vs. heat-bath dynamics) as already known, but even with respect to the order of sites.

cond-mat.stat-mech↗

arXiv1998

Do interactions increase or reduce the conductance of disordered electrons? It depends!

We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. By using an efficient numerical method which is based on exact diagonalization in a truncated basis of Hartree-Fock states we are able to determine the exact low-energy properties of comparatively large systems in the diffusive as well as in the localized regimes. We find that weak interactions increase the d.c. conductance in the localized regime while they decrease the d.c. conductance in the diffusive regime. Strong interactions always decrease the conductance. We also study the localization of single-particle excitations close to the Fermi energy which turns out to be only weakly influenced by the interactions.

cond-mat.str-el↗

arXiv1998

Energy Levels of Quasiperiodic Hamiltonians, Spectral Unfolding, and Random Matrix Theory

We consider a tight-binding Hamiltonian defined on the quasiperiodic Ammann-Beenker tiling. Although the density of states (DOS) is rather spiky, the integrated DOS is quite smooth and can be used to perform spectral unfolding. The effect of unfolding on the integrated level-spacing distribution is investigated for various parts of the spectrum which show different behaviour of the DOS. For energy intervals with approximately constant DOS, we find good agreement with the distribution of the Gaussian orthogonal random matrix ensemble (GOE) even without unfolding. For energy ranges with fluctuating DOS, we observe deviations from the GOE result. After unfolding, we always recover the GOE distribution.

cond-mat.dis-nn↗

arXiv1998

Smoothed universal correlations in the two-dimensional Anderson model

We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the correlation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe these fluctuations and offer a detailed comparison between numerical and analytical calculations for an exhaustive set of two-point correlation functions. We consider parametric correlation functions with an external Aharonov-Bohm flux as a parameter and discuss two cases, namely broken time-reversal invariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density-of-states, velocity and matrix element correlation functions. For the values of smoothing parameter close to the mean level spacing the semiclassical expressions and the numerical results agree quite well in the whole range of the magnetic flux.

cond-mat.dis-nn↗

arXiv1998

Application of random matrix theory to quasiperiodic systems

We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble, and thus differs from the critical level-spacing distribution observed at the metal-insulator transition in the three-dimensional Anderson model of disorder. Our data allow us to see the difference to the Wigner surmise.

cond-mat.dis-nn↗

arXiv1998

Scaling the localisation lengths for two interacting particles in one-dimensional random potentials

Using a numerical decimation method, we compute the localisation length $λ_{2}$ for two onsite interacting particles (TIP) in a one-dimensional random potential. We show that an interaction $U>0$ does lead to $λ_2(U) > λ_2(0)$ for not too large $U$ and test the validity of various proposed fit functions for $λ_2(U)$. Finite-size scaling allows us to obtain infinite sample size estimates $ξ_{2}(U)$ and we find that $ ξ_{2}(U) \sim ξ_2(0)^{α(U)} $ with $α(U)$ varying between $α(0)\approx 1$ and $α(1) \approx 1.5$. We observe that all $ξ_2(U)$ data can be made to coalesce onto a single scaling curve. We also present results for the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs.

cond-mat.str-el↗

arXiv1998

Hartree-Fock based diagonalization: an efficient method for simulating disordered interacting electrons

We present an efficient numerical method for simulating the low-energy properties of disordered many-particle systems. The method which is based on the quantum-chemical configuration interaction approach consists in diagonalizing the Hamiltonian in an energetically truncated basis build of the low-energy states of the corresponding Hartree-Fock Hamiltonian. As an example we investigate the quantum Coulomb glass, a model of spinless electrons in a random potential interacting via long-range Coulomb interaction. We find that the Coulomb interaction increases the conductance of strongly disordered systems but reduces the conductance of weakly disordered systems.

cond-mat.mes-hall↗

arXiv1998

Magnetotransport in Quasilattices

The dc conductance and the Hall voltage of planar arrays of interconnected quantum wires are calculated numerically. Our systems are derived from finite patches of aperiodic graphs, with completely symmetric scatterers placed on their vertices which are interconnected by ideal quantum wires. Already in a periodic square lattice arrangement, quantum interference effects lead to complicated magnetotransport properties related to the Hofstadter butterfly. For rectangular Fibonacci grids and other quasiperiodic lattices, we obtain still more complex fractal patterns. In particular, irrational ratios of edge lengths and of tile areas in our samples destroy the periodicities with respect to the Fermi wave vector and the magnetic flux, respectively.

cond-mat.mes-hall↗

arXiv1998

Localization of Electronic Wave Functions on Quasiperiodic Lattices

We study electronic eigenstates on quasiperiodic lattices using a tight-binding Hamiltonian in the vertex model. In particular, the two-dimensional Penrose tiling and the three-dimensional icosahedral Ammann-Kramer tiling are considered. Our main interest concerns the decay form and the self-similarity of the electronic wave functions, which we compute numerically for periodic approximants of the perfect quasiperiodic structure. In order to investigate the suggested power-law localization of states, we calculate their participation numbers and structural entropy. We also perform a multifractal analysis of the eigenstates by standard box-counting methods. Our results indicate a rather different behaviour of the two- and the three-dimensional systems. Whereas the eigenstates on the Penrose tiling typically show power-law localization, this was not observed for the icosahedral tiling.

cond-mat.dis-nn↗

arXiv1998

Two interacting particles at the metal-insulator transition

To investigate the influence of electronic interaction on the metal-insulator transition (MIT), we consider the Aubry-André (or Harper) model which describes a quasiperiodic one-dimensional quantum system of non-interacting electrons and exhibits an MIT. For a two-particle system, we study the effect of a Hubbard interaction on the transition by means of the transfer-matrix method and finite-size scaling. In agreement with previous studies we find that the interaction localizes some states in the otherwise metallic phase of the system. Nevertheless, the MIT remains unaffected by the interaction. For a long-range interaction, many more states become localized for sufficiently large interaction strength and the MIT appears to shift towards smaller quasiperiodic potential strength.

cond-mat.dis-nn↗

arXiv1998

Transport in disordered interacting systems: Numerical results for one-dimensional spinless electrons

The combined influence of disorder and interactions on the transport properties of electrons in one dimension is investigated. The numerical simulations are carried out by means of the Hartree-Fock-based diagonalization (HFD), a very efficient method to determine the low-energy properties of a disordered many-particle system. We find that the conductance of a strongly localized system can become considerably enhanced by the interactions. The enhancement for long-range interactions is significantly larger than for short-range interactions. In contrast, the conductance of weakly localized systems becomes suppressed by the interactions.

cond-mat.mes-hall↗

arXiv1998

Formation of electron-hole pairs in a one-dimensional random environment

We study the formation of electron-hole pairs for disordered systems in the limit of weak electron-hole interactions. We find that both attractive and repulsive interactions lead to electron-hole pair states with large localization length $λ_{2}$ even when we are in this non-excitonic limit. Using a numerical decimation method to calculate the decay of the Green function along the diagonal of finite samples, we investigate the dependence of $λ_2(U)$ on disorder, interaction strength $U$ and system size. Infinite sample size estimates $ξ_{2}(U)$ are obtained by finite-size scaling. The results show a great similarity to the problem of two interacting electrons in the same random one-dimensional potential.

cond-mat.dis-nn↗

arXiv1998

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, $λ_{2}$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. $λ_{2}(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates $ξ_{2}(U)$ are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite $U$, we find that $ ξ_{2}(U) \sim ξ_2(0)^{β(U)} $ with $β(U)$ varying between $β(0)=1$ and $β(1) \approx 1.5$. We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction.

cond-mat.dis-nn↗

arXiv1998

Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling

We investigate exact eigenstates of tight-binding models on the planar rhombic Penrose tiling. We consider a vertex model with hopping along the edges and the diagonals of the rhombi. For the wave functions, we employ an ansatz, first introduced by Sutherland, which is based on the arrow decoration that encodes the matching rules of the tiling. Exact eigenstates are constructed for particular values of the hopping parameters and the eigenenergy. By a generalized ansatz that exploits the inflation symmetry of the tiling, we show that the corresponding eigenenergies are infinitely degenerate. Generalizations and applications to other systems are outlined.

cond-mat↗

arXiv1998

Two interacting particles in a random potential: The random matrix model revisited

We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we first study numerically how the non-interacting basis is coupled by the interaction. Our results indicate that the typical coupling matrix element decreases significantly faster with increasing single-particle localization length than is assumed in the random matrix model. We further show that even for models where the dependency of the coupling matrix element on the single-particle localization length is correctly described by the corresponding random matrix model its predictions for the localization length can be qualitatively incorrect. These results indicate that the mapping of an interacting random system onto an effective random matrix model is potentially dangerous. We also discuss how Imry's block-scaling picture for two interacting particles is influenced by the above arguments.

cond-mat.dis-nn↗

arXiv1997

Quantum Coulomb glass - Hartree-Fock approximation versus exact diagonalization

We investigate the behavior of disordered interacting electrons in the insulating regime. Our study is based on the quantum Coulomb glass model which is obtained from the classical Coulomb glass by adding hopping matrix elements between neighboring sites. We use two different numerical methods, viz. a Hartree-Fock approximation and an exact diagonalization and compare the results for the tunneling density of states and the localization properties in order to determine the range of validity of the Hartree-Fock method. We find that the Hartree-Fock method gives a good approximation for the density of states for all energies but represents the localization properties correctly close to the Fermi level only. Some consequences for the localization of disordered interacting electrons are discussed.

cond-mat.dis-nn↗

arXiv1997

Quantum Coulomb Glass: Anderson localization in an interacting system

The quantum Coulomb glass model describes disordered interacting electrons on the insulating side of a metal-insulator transition. By taking quantum fluctuations into account it can describe not only the localized limit but also the weakly localized regime. We discuss several possibilities to generalize the concept of Anderson localization to interacting electron systems such as the quantum Coulomb glass and define criteria for localization. The corresponding physical quantities are calculated by numerically exact diagonalization. The results indicate that single-particle excitations close to the Fermi energy become more strongly localized under the influence of interaction.

cond-mat.dis-nn↗

arXiv1997

The two-dimensional Anderson model of localization with random hopping

We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in the center of the band which show critical behavior up to the system size $N= 200 \times 200$ considered. This result is confirmed by an independent analysis of the localization lengths in quasi-1D strips with the help of the transfer-matrix method. Adding a very small additional onsite potential disorder, the critical states become localized.

cond-mat.dis-nn↗