Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis

We compute specific heat of the antiferromagnetic spin-1/2 Heisenberg model on the kagome lattice. We use a recently introduced technique to analyze high-temperature series expansion based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. In the case of kagome-lattice antiferromagnet, this method predicts a low-temperature peak at T/J<0.1.Comment: 6 pages, 5 color figures (.eps), Revtex 4. Change in version 3: Fig. 5 has been corrected (it now shows data for 3 different ground-state energies). The text is unchanged. v4: corrected an error in the temperature scale of Fig. 5. (text unchanged

Critical Conductance of a Mesoscopic System: Interplay of the Spectral and Eigenfunction Correlations at the Metal-Insulator Transition

We study the system-size dependence of the averaged critical conductance $g(L)$ at the Anderson transition. We have: (i) related the correction $\delta g(L)=g(\infty)-g(L)\propto L^{-y}$ to the spectral correlations; (ii) expressed $\delta g(L)$ in terms of the quantum return probability; (iii) argued that $y=\eta$ -- the critical exponent of eigenfunction correlations. Experimental implications are discussed.Comment: minor changes, to be published in PR

Strong eigenfunction correlations near the Anderson localization transition

We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of Anderson transition their mutual overlap is still found to be of the same order as self-overlap as long as energy separation is smaller than a critical value. The latter fact explains robustness of the Wigner-Dyson level statistics everywhere in the phase of extended states. The same picture is expected to hold for usual d-dimensional conductors, ensuring the $s^{\beta}$ form of the level repulsion at critical point.Comment: 4 pages, RevTe

Field evolution of the magnetic structures in Er2_2Ti2_2O7_7 through the critical point

We have measured neutron diffraction patterns in a single crystal sample of the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase (T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the [110] direction. We determine all the characteristics of the magnetic structure throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er moments align along the field at $H_c$ and their values reach a minimum. Using a four-sublattice self-consistent calculation, we show that the evolution of the magnetic structure and the value of the critical field are rather well reproduced using the same anisotropic exchange tensor as that accounting for the local paramagnetic susceptibility. In contrast, an isotropic exchange tensor does not match the moment variations through the critical point. The model also accounts semi-quantitatively for other experimental data previously measured, such as the field dependence of the heat capacity, energy of the dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure

Dzyaloshinski-Moriya interactions in the kagome lattice

The kagom\'e lattice exhibits peculiar magnetic properties due to its strongly frustated cristallographic structure, based on corner sharing triangles. For nearest neighbour antiferromagnetic Heisenberg interactions there is no Neel ordering at zero temperature both for quantum and classical s pins. We show that, due to the peculiar structure, antisymmetric Dzyaloshinsky-Moriya interactions (${\bf D} . ({\bf S}_i \times {\bf S}_j)$) are present in this latt ice. In order to derive microscopically this interaction we consider a set of localized d-electronic states. For classical spins systems, we then study the phase diagram (T, D/J) through mean field approximation and Monte-Carlo simulations and show that the antisymmetric interaction drives this system to ordered states as soon as this interaction is non zero. This mechanism could be involved to explain the magnetic structure of Fe-jarosites.Comment: 4 pages, 2 figures. Presented at SCES 200

Point-Contact Conductances from Density Correlations

We formulate and prove an exact relation which expresses the moments of the two-point conductance for an open disordered electron system in terms of certain density correlators of the corresponding closed system. As an application of the relation, we demonstrate that the typical two-point conductance for the Chalker-Coddington model at criticality transforms like a two-point function in conformal field theory.Comment: 4 pages, 2 figure

Wave-packet dynamics at the mobility edge in two- and three-dimensional systems

We study the time evolution of wave packets at the mobility edge of disordered non-interacting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory. In particular, we find that the $k$-th moment of the probability density $(t)$ scales like $t^{k/d}$ in $d$ dimensions. The return probability $P(r=0,t)$ scales like $t^{-D_2/d}$, with the generalized dimension of the participation ratio $D_2$. For long times and short distances the probability density of the wave packet shows power law scaling $P(r,t)\propto t^{-D_2/d}r^{D_2-d}$. The numerical calculations were performed on network models defined by a unitary time evolution operator providing an efficient model for the study of the wave packet dynamics.Comment: 4 pages, RevTeX, 4 figures included, published versio

Modeling Disordered Quantum Systems with Dynamical Networks

It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-{\em dynamical} models, which then allow for an investigation of dynamical and spectral aspects. This concept is exemplified by the Chalker-Coddington model for the Quantum Hall effect and a three-dimensional generalization of it. We simulate phase coherent diffusion of wave packets and consider spatial and spectral correlations of network eigenstates as well as the distribution of (quasi-)energy levels. Apart from that it is demonstrated how network models can be used to determine two-point conductances. Our numerical calculations for the three-dimensional model at the Metal-Insulator transition point delivers among others an anomalous diffusion exponent of $\eta = 3 - D_2 = 1.7 \pm 0.1$. The methods presented here in detail have been used partially in earlier work.Comment: 16 pages, Rev-TeX. to appear in Int. J. Mod. Phys.

Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility $\chi$ at the mobility edge, $\chi=\eta/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.Comment: 5 pages, RevTeX, 3 figures, Postscript, strongly revised version to be published in PR

Universal eigenvector statistics in a quantum scattering ensemble

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector correlations corresponding to eigenvalues in the center of the support of the density of states in the complex plane are described by an expression recently derived for Ginibre's ensemble of random non-Hermitian matrices.Comment: 4 pages, 5 figure