Numerical study of quantum percolation

We study the density of states and the optical conductivity of the classical double-exchange model on a site percolated cluster.Comment: 2 pages, 2 figures, submitted to SCES 200

Compass model on a ladder and square clusters

We obtained exact heat capacities of the quantum compass model on the square L x L clusters with L=2,3,4,5 using Kernel Polynomial Method and compare them with heat capacity of a large compass ladder. Intersite correlations found in the ground state for these systems demonstrate that the quantum compass model differs from its classical version.Comment: 4 pages, 2 figures, submitted to J. Phys. Conf. Serie

Quantum to classical crossover in the 2D easy-plane XXZ model

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters $\Delta$. In the easy--plane ferromagnetic region $(-1< \Delta < 0)$, the longitudinal correlators of spins at distance $r$ change sign at a finite temperature $T_0(\Delta, {\bf r})$. This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.Comment: 4 pages, 6 figures, Contribution to the Ising Centennial Colloquium, ICM2000, Belo Horizonte, Brazil, August 200

The fate of topological-insulator surface states under strong disorder

Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered "surface" states emerge in the sample beneath the disordered surface layer, which can be understood in terms of an interface between a topological and an Anderson insulator. Together, this demonstrates the drastic effect of disorder on topological surface states, which cannot be captured within effective two-dimensional models for the surface states alone.Comment: 4.3 pages, 4 fig

Characterisation of Anderson localisation using distributions

We examine the use of distributions in numerical treatments of Anderson localisation and supply evidence that treating exponential localisation on Bethe lattices recovers the overall picture known from hypercubic lattices in 3d.Comment: 2 pages, 2 figures, submitted to SCES'0

Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach

We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way that allows for their direct implementation on a computer. Within the Fermionic basis approach a huge class of stationary reduced density matrices, compatible with the integrable structure of the model, assumes a factorized form. This means that all expectation values of local operators and all two-point functions, in particular, can be represented as multivariate polynomials in only two functions $\rho$ and $\omega$ and their derivatives with coefficients that are rational in the deformation parameter $q$ of the model. These coefficients are of `algebraic origin'. They do not depend on the choice of the density matrix, which only impacts the form of $\rho$ and $\omega$. As an example we work out in detail the case of the grand canonical ensemble at temperature $T$ and magnetic field $h$ for $q$ in the critical regime. We compare our exact results for the fourth-neighbour two-point functions with asymptotic formulae for $h, T = 0$ and for finite $h$ and $T$

Bose-Einstein condensation of magnons in TlCuCl3_3

A quantitative study of the field-induced magnetic ordering in TlCuCl$_3$ in terms of a Bose-Einstein condensation (BEC) of magnons is presented. It is shown that the hitherto proposed simple BEC scenario is in quantitative and qualitative disagreement with experiment. It is further shown that even very small Dzyaloshinsky-Moriya interactions or a staggered $g$ tensor component of a certain type can change the BEC picture qualitatively. Such terms lead to a nonzero condensate density for all temperatures and a gapped quasiparticle spectrum. Including this type of interaction allows us to obtain good agreement with experimental data.Comment: 2 pages, 2 figures, submitted to SCES'0

On the theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet

We analyze the problem of microwave absorption by the Heisenberg-Ising magnet in terms of shifted moments of the imaginary part of the dynamical susceptibility. When both, the Zeeman field and the wave vector of the incident microwave, are parallel to the anisotropy axis, the first four moments determine the shift of the resonance frequency and the line width in a situation where the frequency is varied for fixed Zeeman field. For the one-dimensional model we can calculate the moments exactly. This provides exact data for the resonance shift and the line width at arbitrary temperatures and magnetic fields. In current ESR experiments the Zeeman field is varied for fixed frequency. We show how in this situation the moments give perturbative results for the resonance shift and for the integrated intensity at small anisotropy as well as an explicit formula connecting the line width with the anisotropy parameter in the high-temperature limit.Comment: 4 page