Local distribution approach to disordered binary alloys

We study the electronic structure of the binary alloy and (quantum) percolation model. Our study is based on a self-consistent scheme for the distribution of local Green functions. We obtain detailed results for the density of states, from which the phase diagram of the binary alloy model is constructed, and discuss the existence of a quantum percolation threshold.Comment: 9 pages, 8 figures. A few minor changes, 1 figure adde

The Kernel Polynomial Method

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad application not only in physics. Representative examples from the fields of disordered systems, strongly correlated electrons, electron-phonon interaction, and quantum spin systems we discuss in detail. In addition, we illustrate how the Kernel Polynomial Method is successfully embedded into other numerical techniques, such as Cluster Perturbation Theory or Monte Carlo simulation.Comment: 32 pages, 17 figs; revised versio

Solution of the Holstein polaron anisotropy problem

We study Holstein polarons in three-dimensional anisotropic materials. Using a variational exact diagonalization technique we provide highly accurate results for the polaron mass and polaron radius. With these data we discuss the differences between polaron formation in dimension one and three, and at small and large phonon frequency. Varying the anisotropy we demonstrate how a polaron evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby resolve the issue of polaron stability in quasi-one-dimensional substances and clarify to what extent such polarons can be described as one-dimensional objects. We finally show that even the local Holstein interaction leads to an enhancement of anisotropy in charge carrier motion.Comment: 6 pages, 7 figures; extended version accepted for publication in Phys. Rev.

Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator

In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum. The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems. We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from the bulk. We implement this scenario for a simple model of an anomalous Floquet insulator with Hermitian and non-Hermitian boundaries, and discuss the relevance of our construction for the experimental realization of non-Hermitian topological phases that connect dimensions one and two.Comment: 7 pages, 4 figure