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

Magnetism in Rare Earth Quasicrystals: RKKY Interactions and Ordering

We study magnetism in simple models for rare earth quasicrystals by means of a two-step theoretical approach. First, we compute RKKY interactions from a tight-binding Hamiltonian defined on a two-dimensional quasiperiodic tiling. Second, we examine the statistical mechanics of Ising spins coupled via these interactions using Monte Carlo simulations. We find the emergence of strongly coupled spin clusters with significantly weaker inter-cluster coupling, and a transition to a low-temperature phase that has long-range order evidenced by a finite domain wall tension.Comment: restructuring of paper and update of numerical results, 5 pages, 4 figure

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

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

Deconfinement transitions in a generalised XY model

We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz-Thouless (KT) transitions for both the half-vortices and ordinary vortices, as well as an Ising-type transition. There also occurs an unusual deconfining phase transition, where the disordered to superfluid transition is of Ising rather than KT type. We show by analytical arguments and extensive numerical simulations that there is a point in the phase diagram where the KT transition line meets the deconfining Ising phase transition. We find that the latter extends into the disordered phase not as a phase transition, but rather solely as a deconfinement transition. It is best understood in the dual height model, where on one side of the transition height steps are bound into pairs while on the other they are unbound. We also extend the phase diagram of the dual model, finding both O(2) loop model and antiferromagnetic Ising transitions.Comment: 19 pages. v2: references added and minor changes. Appears in "John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday

Electron Interactions and Transport Between Coupled Quantum Hall Edges

We examine the effects of electron-electron interactions on transport between edge states in a multilayer integer quantum Hall system. The edge states of such a system, coupled by interlayer tunneling, form a two-dimensional, chiral metal at the sample surface. We calculate the temperature-dependent conductivity and the amplitude of conductance fluctuations in this chiral metal, treating Coulomb interactions and disorder exactly in the weak-tunneling limit. We find that the conductivity increases with increasing temperature, as observed in recent experiments, and we show that the correlation length characterising conductance fluctuations varies inversely with temperature.Comment: 4 pages, 2 figures, typos corrected, Ref. 17 added, minor changes made for publicatio

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