arXiv subjects

M. Schreiber

Publications and source records attributed to M. Schreiber.

61 records · Page 4Linked to original sources

arXiv1999

Combinatorial Optimization by Iterative Partial Transcription

A procedure is presented which considerably improves the performance of local search based heuristic algorithms for combinatorial optimization problems. It increases the average `gain' of the individual local searches by merging pairs of solutions: certain parts of either solution are transcribed by the related parts of the respective other solution, corresponding to flipping clusters of a spin glass. This iterative partial transcription acts as a local search in the subspace spanned by the differing components of both solutions. Embedding it in the simple multi-start-local-search algorithm and in the thermal-cycling method, we demonstrate its effectiveness for several instances of the traveling salesman problem. The obtained results indicate that, for this task, such approaches are far superior to simulated annealing.

cond-mat.dis-nn↗

arXiv1998

Pseudogaps and magnetic properties of the two-dimensional t-J model

We apply the modified spin-wave theory with the constraint of zero staggered magnetization to investigate normal-state spectral and magnetic properties of the 2D t-J model in the paramagnetic state. A set of self-energy equations for hole and magnon Green's functions is solved numerically in the self-consistent Born approximation. The constraint can be fulfilled in the ranges of hole concentrations 0.02 < x < 0.17 and temperatures T < 150 K. In this region the hole spectrum differs from a conventional metallic spectrum which is manifested in the variation with x of the quasiparticle weights of states and in the violation of Luttinger's theorem. With decreasing x from x = 0.17 hidden parts appear in the hole Fermi surface which can be interpreted as the opening of a pseudogap near (pi,0). Obtained size, symmetry and concentration dependence of the pseudogap are in agreement with photoemission data in Bi2212. Calculated temperature dependencies of the spin correlation length, spin-lattice relaxation times at the Cu and O sites, and static susceptibility are typical for the quantum disordered regime with a pseudogap in the spectrum of magnetic excitations. These quantities are in qualitative and in some cases in quantitative agreement with experiment in underdoped YBa2Cu3O(6+y). At x > 0.12 the considered phase borders the phase of conventional metal.

cond-mat.str-el↗

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↗

arXiv1997

Coulomb glass simulations: Creation of a set of low-energy many-particle states, non-ergodic effects in the specific heat

We have implemented a new numerical method to obtain the low-energy many-particle states of the Coulomb glass. First, this method creates an initial set of low-energy states by a hybrid of local search and simulated annealing approaches. Then, systematically investigating the surroundings of the states found, this set is completed. The transition rates between these states are calculated. The connectivity of the corresponding graph is analysed in dependence on temperature and duration of measurement. We study how the formation of clusters is reflected in the specific heat as non-ergodic effects.

cond-mat.dis-nn↗

arXiv1994

Does a magnetic field modify the critical behaviour at the metal-insulator transition in 3-dimensional disordered systems?

The critical behaviour of 3-dimensional disordered systems with magnetic field is investigated by analyzing the spectral fluctuations of the energy spectrum. We show that in the thermodynamic limit we have two different regimes, one for the metallic side and one for the insulating side with different level statistics. The third statistics which occurs only exactly at the critical point is {\it independent} of the magnetic field. The critical behaviour which is determined by the symmetry of the system {\it at} the critical point should therefore be independent of the magnetic field.

cond-mat↗

arXiv1994

Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $ν=1.34$ are computed.

cond-mat↗