Valence Bond Entanglement and Fluctuations in Random Singlet Phases

The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain can be viewed as a strongly fluctuating liquid of valence bonds, while in disordered chains these bonds lock into random singlet states on long length scales. We show that this phenomenon can be studied numerically, even in the case of weak disorder, by calculating the mean value of the number of valence bonds leaving a block of $L$ contiguous spins (the valence-bond entanglement entropy) as well as the fluctuations in this number. These fluctuations show a clear crossover from a small $L$ regime, in which they behave similar to those of the uniform model, to a large $L$ regime in which they saturate in a way consistent with the formation of a random singlet state on long length scales. A scaling analysis of these fluctuations is used to study the dependence on disorder strength of the length scale characterizing the crossover between these two regimes. Results are obtained for a class of models which include, in addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical 1D transverse-field Ising model and chains of interacting non-Abelian anyons.Comment: 8 pages, 6 figure

Comparison of averages of flows and maps

It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to permanent chaos, results obtained from the Poincare map can even be qualitatively incorrect. The reason is that the return time between intersections on the Poincare surface becomes relevant. However, after introducing a true-time Poincare map, quantities known from the usual Poincare map, such as conditionally invariant measure and natural measure, can be generalized to this case. Escape rates and averages, e.g. Liapunov exponents and drifts can be determined correctly using these novel measures. Significant differences become evident when we compare with results obtained from the usual Poincare map.Comment: 4 pages in Revtex with 2 included postscript figures, submitted to Phys. Rev.

Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles

One-dimensional chains of non-Abelian quasiparticles described by $SU(2)_k$ Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to $k \to \infty$). For $k=2$ this phase provides a random singlet description of the infinite randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size $L$ in these phases scales as $S_L \simeq \frac{\ln d}{3} \log_2 L$ for large $L$, where $d$ is the quantum dimension of the particles.Comment: 4 pages, 4 figure

Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state

We derive a relationship between the optical conductivity scattering rate 1/\tau(\omega) and the electron-boson spectral function \alpha^2F(\Omega) valid for the case when the electronic density of states, N(\epsilon), cannot be taken as constant in the vicinity of the Fermi level. This relationship turned out to be useful for analyzing the experimental data in the pseudogap state of cuprate superconductors.Comment: 8 pages, RevTeX4, 1 EPS figure; final version published in PR

A burst with double radio spectrum observed up to 212 GHz

We study a solar flare that occurred on September 10, 2002, in active region NOAA 10105 starting around 14:52 UT and lasting approximately 5 minutes in the radio range. The event was classified as M2.9 in X-rays and 1N in H\alpha. Solar Submillimeter Telescope observations, in addition to microwave data give us a good spectral coverage between 1.415 and 212 GHz. We combine these data with ultraviolet images, hard and soft X-rays observations and full-disk magnetograms. Images obtained from Ramaty High Energy Solar Spectroscopic Imaging data are used to identify the locations of X-ray sources at different energies and to determine the X-ray spectrum, while ultra violet images allow us to characterize the coronal flaring region. The magnetic field evolution of the active region is analyzed using Michelson Doppler Imager magnetograms. The burst is detected at all available radio-frequencies. X-ray images (between 12 keV and 300 keV) reveal two compact sources and 212 GHz data, used to estimate the radio source position, show a single compact source displaced by 25" from one of the hard X-ray footpoints. We model the radio spectra using two homogeneous sources, and combine this analysis with that of hard X-rays to understand the dynamics of the particles. Relativistic particles, observed at radio wavelengths above 50 GHz, have an electron index evolving with the typical soft-hard-soft behaviour.Comment: Submitted to Solar Physics, 20 pages, 8 fugure