A Monte Carlo Study of Correlations in Quantum Spin Ladders

We study antiferromagnetic spin--1/2 Heisenberg ladders, comprised of $n_c$ chains ($2 \leq n_c \leq 6$) with ratio $J_{\bot}/J_{\|}$ of inter-- to intra--chain couplings. From measurements of the correlation function we deduce the correlation length $\xi(T)$. For even $n_c$, the static structure factor exhibits a peak at a temperature below the corresponding spin gap. Results for isotropically coupled ladders ($J_{\bot}/J_{\|} = 1$) are compared to those for the single chain and the square lattice. For $J_{\bot}/J_{\|} \leq 0.5$, the correlation function of the two--chain ladder is in excellent agreement with analytic results from conformal field theory, and $\xi(T)$ exhibits simple scaling behavior.Comment: 4 pages, 5 EPS figures, submitted to Phys. Rev. Let

Thickness-Magnetic Field Phase Diagram at the Superconductor-Insulator Transition in 2D

The superconductor-insulator transition in ultrathin films of amorphous Bi was tuned by changing the film thickness, with and without an applied magnetic field. The first experimentally obtained phase diagram is mapped as a function of thickness and magnetic field in the T=0 limit. A finite size scaling analysis has been carried out to determine the critical exponent product vz, which was found to be 1.2 for the zero field transition, and 1.4 for the finite field transition. Both results are different from the exponents found for the magnetic field tuned transition in the same system, 0.7.Comment: 4 pages, 4 figure

Critical behavior at superconductor-insulator phase transitions near one dimension

I argue that the system of interacting bosons at zero temperature and in random external potential possesses a simple critical point which describes the proliferation of disorder-induced topological defects in the superfluid ground state, and which is located at weak disorder close to and above one dimension. This makes it possible to address the critical behavior at the superfluid-Bose glass transition in dirty boson systems by expanding around the lower critical dimension d=1. Within the formulated renormalization procedure near d=1 the dynamical critical exponent is obtained exactly and the correlation length exponent is calculated as a Laurent series in the parameter \sqrt{\epsilon}, with \epsilon=d-1: z=d, \nu=1/\sqrt{3\epsilon} for the short range, and z=1, \nu=\sqrt{2/3\epsilon}, for the long-range Coulomb interaction between bosons. The identified critical point should be stable against the residual perturbations in the effective action for the superfluid, at least in dimensions 1\leq d \leq 2, for both short-range and Coulomb interactions. For the superfluid-Mott insulator transition in the system in a periodic potential and at a commensurate density of bosons I find \nu=(1/2\sqrt{\epsilon})+ 1/4+O(\sqrt{\epsilon}), which yields a result reasonably close to the known XY critical exponent in d=2+1. The critical behavior of the superfluid density, phonon velocity and the compressibility in the system with the short-range interactions is discussed.Comment: 23 pages, 1 Postscript figure, LaTe

Quantum magnetism in the stripe phase: bond- versus site order

It is argued that the spin dynamics in the charge-ordered stripe phase might be revealing with regards to the nature of the anomalous spin dynamics in cuprate superconductors. Specifically, if the stripes are bond ordered much of the spin fluctuation will originate in the spin sector itself, while site ordered stripes require the charge sector as the driving force for the strong quantum spin fluctuations.Comment: 4 pages, 3 figures, LaTe

Numerical Calculations of the B1g Raman Spectrum of the Two-Dimensional Heisenberg Model

The B1g Raman spectrum of the two-dimensional S=1/2 Heisenberg model is discussed within Loudon-Fleury theory at both zero and finite temperature. The exact T=0 spectrum for lattices with up to 6*6 sites is computed using Lanczos exact diagonalization. A quantum Monte Carlo (QMC) method is used to calculate the corresponding imaginary-time correlation function and its first two derivatives for lattices with up to 16*16 spins. The imaginary-time data is continued to real frequency using the maximum-entropy method, as well as a fit based on spinwave theory. The numerical results are compared with spinwave calculations for finite lattices. There is a surprisingly large change in the exact spectrum going from 4*4 to 6*6 sites. In the former case there is a single dominant two-magnon peak at frequency w/J appr. 3.0, whereas in the latter case there are two approximately equal-sized peaks at w/J appr. 2.7 and 3.9. This is in good qualitative agreement with the spinwave calculations including two-magnon processes on the same lattices. Both the Lanczos and the QMC results indicate that the actual infinite-size two-magnon profile is broader than the narrow peak obtained in spinwave theory, but the positions of the maxima agree to within a few percent. The higher-order contributions present in the numerical results are merged with the two-magnon profile and extend up to frequencies w/J appr. 7. The first three frequency cumulants of the spectrum are in excellent agreement with results previously obtained from a series expansion around the Ising limit. Typical experimental B1g$ spectra for La2CuO4 are only slightly broader than what we obtain here. The exchange constant extracted from the peak position is J appr. 1400K, in good agreement with values obtained from neutron scattering and NMR experiments.Comment: 15 pages, Revtex, 13 PostScript figure

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

Spin dynamics of the 2D spin 1/2 quantum antiferromagnet copper deuteroformate tetradeuterate (CFTD)

The magnetic excitation spectrum in the two-dimensional (2D) S = 1/2 Heisenberg antiferromagnet copper deuteroformate tetradeuterate has been measured for temperatures up to T similar to J/2, where J = 6.31 +/- 0.02 meV is the 2D exchange coupling. For T << J, a dispersion of the zone boundary energy is observed, which is attributed to a wave vector dependent quantum renormalization. At higher temperatures, spin-wavelike excitations persist, but are found to broaden and soften. By combining our data with numerical calculations, and with existing theoretical work, a consistent description of the behavior of the model system is found over the whole temperature interval investigated