S(k) for Haldane Gap Antiferromagnets: Large-scale Numerical Results vs. Field Theory and Experiment

The structure function, S(k), for the s=1, Haldane gap antiferromagnetic chain, is measured accurately using the recent density matrix renormalization group method, with chain-length 100. Excellent agreement with the nonlinear $\sigma$ model prediction is obtained, both at $k\approx \pi$ where a single magnon process dominates and at $k\approx 0$ where a two magnon process dominates. We repeat our calculation with crystal field anisotropy chosen to model NENP, obtaining good agreement with both field theory predictions and recent experiments. Correlation lengths, gaps and velocities are determined for both polarizations.Comment: 11 pages, 3 postscript figures included, REVTEX 3.0, UBCTP-93-02

Impurities in s=1s=1 Heisenberg Antiferromagnets

The $s=1$ Heisenberg Antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with $J'\ne J$ at the center of an even-length open chain is considered. Using the density matrix renormalization group method we find that, for sufficiently strong or weak $J'$, a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on $s=1/2$ chain-end excitations, both in the weak and strong coupling limit. In a region around the uniform limit, $J'=J$, no states are found with energy below the Haldane gap. Secondly, a $s=1/2$ impurity at the center of an otherwise even-length open chain is considered. The coupling to the $s=1/2$ impurity is varied. Bound states in the Haldane gap are found {\it only} for sufficiently weak (antiferromagnetic) coupling. For a $s=1/2$ impurity coupled with a strong (antiferromagnetic) bond, {\it no} states are found in the Haldane. Our results are in good qualitative agreement with recent experiments on doped NENP and Y$_2$BaNiO$_5$.Comment: 29 pages, RevTeX 3.0, 12 uuencoded postscript figures include

Equal Time Correlations in Haldane Gap Antiferromagnets

The $S=1$ antiferromagnetic Heisenberg chain both with and without single ion anisotropy is studied. Using the recently proposed density matrix renormalization group technique we calculate the energy gaps as well as several different correlation functions. The two gaps, $\Delta_{||}, \Delta_\perp$, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions derived from the nonlinear sigma model and a free boson model. We also study the $S=1/2$ excitations that occur at the ends of open chains; in particular we study the behavior associated with open boundary conditions, using a model of $S=1/2$ spins coupled to the free bosons.Comment: 32 pages, uufiles encoded REVTEX 3.0, 19 postscript figures included, UBCTP-93-02

Integer Quantum Hall Effect in Double-Layer Systems

We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models and on transfer matrix calculations for phenomenological network models. The microscopic calculations indicate a crossover regime for weak interlayer tunneling in which the correlation length exponent appears to increase. Comparison of network model calculations with microscopic calculations casts doubt on their generic applicability.Comment: 14 pages, 12 figures included, RevTeX 3.0 and epsf. Additional reference

The superconductor-insulator transition in 2D dirty boson systems

Universal properties of the zero temperature superconductor-insulator transition in two-dimensional amorphous films are studied by extensive Monte Carlo simulations of bosons in a disordered medium. We report results for both short-range and long-range Coulomb interactions for several different points in parameter space. In all cases we observe a transition from a superconducting phase to an insulating Bose glass phase. {}From finite-size scaling of our Monte Carlo data we determine the universal conductivity $\sigma^*$ and the critical exponents at the transition. The result $\sigma^* = (0.55 \pm 0.06) (2e)^2/h$ for bosons with long-range Coulomb interaction is roughly consistent with experiments reported so far. We also find $\sigma^* = (0.14 \pm 0.03) (2e)^2/h$ for bosons with short-range interactions.Comment: Revtex 3.0, 54 pages, 17 figures included, UBCTP-93-01