arXiv subjects

R. A. Roemer

Publications and source records attributed to R. A. Roemer.

26 records · Page 2Linked to original sources

arXiv1999

Phase diagram of the three-dimensional Anderson model of localization with random hopping

We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen randomly according to $t_{ij} \in [c-1/2, c + 1/2]$. We find that the off-diagonal disorder is not strong enough to localize all states in the spectrum in contradistinction to the usual case of diagonal disorder. Thus for any off-diagonal disorder, there exist extended states and, consequently, the TMM converges very slowly. From the TMM results we compute critical exponents of the metal-insulator transitions (MIT), the mobility edge $E_c$, and study the energy-disorder phase diagram.

cond-mat.dis-nn↗

arXiv1999

Numerical results for two interacting particles in a random environment

Much evidence has been collected to date which shows that repulsive electron-electron interaction can lead to the formation of particle pairs in a one-dimensional random energy landscape. The localization length λ_2 of these pair states is finite, but larger than the localization length λ_1 of the individual particles. After a short review of previous work, we present numerical evidence for this effect based on an analysis of the interaction matrix elements and an application of the decimation method. The results based on the decimation method for a two-dimensional disordered medium support the localization-delocalization transition of pair states predicted recently.

cond-mat.dis-nn↗

arXiv1999

Transport properties near the Anderson transition

The electronic transport properties in the presence of a temperature gradient in disordered systems near the metal-insulator transition [MIT] are considered. The d.c. conductivity $σ$, the thermoelectric power $S$, the thermal conductivity $K$ and the Lorenz number $L_0$ are calculated for the three-dimensional Anderson model of localization using the Chester-Thellung-Kubo-Greenwood formulation of linear response. We show that $σ$, S, K and $L_0$ can be scaled to one-parameter scaling curves with a single scaling paramter $k_BT/|{μ-E_c}/E_c|$.

cond-mat.dis-nn↗

arXiv1999

Thermoelectric Transport Properties in Disordered Systems Near the Anderson Transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition [MIT]. In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L_0 on temperature T. We first calculate the T dependence of the chemical potential from the number density of electrons at the MIT using averaged density of state obtained by diagonalization. Without any additional approximation, we determine from the chemical potential the behavior of S, K and L_0 at low T as the MIT is approached. We find that the d.c. conductivity and K decrease to zero at the MIT as T -> 0 and show that S does not diverge. Both S and L_0 become temperature independent at the MIT and depend only on the critical behavior of the conductivity.

cond-mat.dis-nn↗

arXiv1998

Low Temperature Behavior of the Thermopower in Disordered Systems near the Anderson Transition

We investigate the behavior of the thermoelectric power [S] in disordered systems close to the Anderson-type metal-insulator transition [MIT] at low temperatures. In the literature, we find contradictory results for S. It is either argued to diverge or to remain a constant as the MIT is approached. To resolve this dilemma, we calculate the number density of electrons at the MIT in disordered systems using an averaged density of states obtained by diagonalizing the three-dimensional Anderson model of localization. From the number density we obtain the temperature dependence of the chemical potential necessary to solve for S. Without any additional approximation, we use the Chester-Thellung-Kubo-Greenwood formulation and numerically obtain the behavior of S at low T as the Anderson transition is approached from the metallic side. We show that indeed S does not diverge.

cond-mat.dis-nn↗

arXiv1998

The Anderson model of localization: a challenge for modern eigenvalue methods

We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.

physics.comp-ph↗

arXiv1997

Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models

We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random matrix theory. Properly taking into account the symmetries of models defined on various finite approximants of quasiperiodic tilings, we find that the underlying universal level-spacing distribution is given by the Wigner-Dyson distribution of the Gaussian orthogonal random matrix ensemble. Our data allow us to see the differences between the Wigner surmise and the exact level-spacing distribution. In particular, our result differs from the critical level-spacing distribution computed at the metal-insulator transition in the three-dimensional Anderson model of disorder.

cond-mat.dis-nn↗

arXiv1995

GAPS IN THE HEISENBERG-ISING MODEL

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $π$. For half-filling, the gap closes at special values of the anisotropy $Δ= \cos(π/Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $Δ$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $Δ\sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $Δ$ and the corresponding perturbation expansion in $Δ$ shows a remarkable cancellation of various diagrams.

cond-mat↗