Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis

We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as the trial state, but a more rapid convergence can be obtained using a good variational state. As an alternative to first carrying out a time consuming variational Monte Carlo calculation, we show that a very good trial state can be generated in an iterative fashion in the course of the simulation itself. We also show how the properties of the valence bond basis enable calculations of quantities that are difficult to obtain with the standard basis of Sz eigenstates. In particular, we discuss quantities involving finite-momentum states in the triplet sector, such as the dispersion relation and the spectral weight of the lowest triplet.Comment: 15 pages, 7 figures, for the proceedings of "Computer Simulation Studies in Condensed Matter Physics XX

Master equation approach to computing RVB bond amplitudes

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes are radially symmetric and fall off as 1/r^3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.Comment: 8 pages, 7 figure

Rate constants and Arrhenius parameters for the reactions of OH radicals and Cl atoms with CF3CH2OCHF2, CF3CHClOCHF2 and CF3CH2OCClF2, using the discharge-flow/resonance fluorescence method

Rate constants have been determined for the reactions of OH radicals and Cl atoms with the three partially halogenated methyl-ethyl ethers, CF$_3$CH$_2$OCHF$_2$, CF$_3$CHClOCHF$_2$ and CF$_3$CH$_2$OCClF$_2$, using discharge-flow techniques to generate the OH radicals and the Cl atoms and resonance fluorescence to observe changes in their relative concentrations in the presence of added ether. For each combination of radical and ether, experiments were carried out at three temperatures between 292 and 410 K, yielding the following Arrhenius expressions for the rate constants within this range of temperature: OH + CF$_3$CH$_2$OCHF$_2$: $k$ = (2.0$\pm$0.8) $\times$ 10$^{-11}$ exp( – 2110 $\pm$ 150 K / T) cm$^3$ molecule$^{-1}$ s$^{-1}$ OH + CF$_3$CHClOCHF$_2$: $k$ = (4.5 $\pm$ 1.3) $\times$ 10$^{-13}$ exp( – 940 $\pm$ 100 K / T) cm$^3$ molecule$^{-1}$ s$^{-1}$ OH + CF$_3$CH$_2$OCClF$_2$: $k$ = (1.6 $\pm$ 0.6) $\times$ 10$^{-12}$ exp( – 1100 $\pm$ 125 K / T) cm$^3$ molecule$^{-1}$ s$^{-1}$ Cl + CF$_3$CH$_2$OCHF$_2$: $k$ = (6.1 $\pm$ 1.4) $\times$ 10$^{-12}$ exp( – 1830 $\pm$ 90 K / T) cm$^3$ molecule$^{-1}$ s$^{-1}$ Cl + CF$_3$CHClOCHF$_2$: $k$ = (7.8 $\pm$ 2.6) $\times$ 10$^{-11}$ exp( – 2980 $\pm$ 130 K / T) cm$^3$ molecule$^{-1}$ s$^{-1}$ Cl + CF$_3$CH$_2$OCClF$_2$: $k$ = (2.2 $\pm$ 0.2) $\times$ 10$^{-11}$ exp( – 2700 $\pm$ 40 K / T) cm$^3$ molecule$^{-1}$ s$^{-1}$ The results are compared with those obtained previously for the same and related reactions of OH radicals and Cl atoms, and the atmospheric implications of the results are considered briefly

Hardiness in the apple as correlated with structure and composition

The breeding of hardy apples is naturally such a long time proposition that it would be a distinct advantage if by microscopic examination of the wood, by mechanical tests, or by other observations the hardiness of a tree could be determined while it was still in the nursery, The following is a summary of the facts brought out in the investigation of Hardiness in the Apple as Correlated with Structure and Composition. 1. The cutting, compression and penetration tests seemed to indicate some correlation between hardiness and hardness, but exceptions were found. 2, Twigs from northern sections, except the forms of Metlus rivularis, Red June and Patten, were no harder than twigs from Iowa and further south. 3, Specific gravity tests of dry wood showing density corresponded very closely with the mechanical tests showing hardness, indicating that the two tests are fairly accurate means to the same end. 4. Variat ions in the specific gravity of twigs of the same variety from different sources were noted, as was also the case in the mechanical tests. Twigs of the same variety from the same source gave pretty uniform results. 5. The specific gravity of twigs varies, to some extent depending upon what part of the twig is used. The tenderer varieties, which mature a little later in the summer, gave the greatest specific gravity a short distance back of the tip; earlier maturing varieties increased in specific gravity in proportion to the distance from the tip. As the tests were made in July this difference is in all probability due to the difference in the maturing of the twigs used. 6. The maturity of the wood at the time cold weather sets in undoubtedly has a most important bearing upon the ability of the tree to withstand cold. 7. By noting the formation of terminal buds and the time of leaf fall a pretty accurate idea of maturity can be secured, except in case of a few varieties. 8. The hardier varieties on the average had a slightly lower moisture content than the more tender varieties. 9. The difference in water content can be explained partly at least by the fact that the more tender sorts evaporate water more readily than do the hardy varieties. Freezing tends to dry the twig out, and after a period of very cold weather the twigs of the hardy varieties are generally found to contain the most moisture. 10. The rate of evaporation is due in part to small differences in thickness and structure of bark, including differences in the number of cutinized layers. 11. Most of the hardy varieties contained a large amount of starch stored in the pith and medullary rays. The Malus ioensis, however, proved to be an exception in this regard. 12. Large, thick petals are correlated with hardiness, although the converse of this is not always true. 13. The results of the freezing experiments show that within the limits observed a sudden drop in temperature is more injurious than the actual degree of cold. 14. While all twigs not previously dried were injured to some extent when held in a temperature of -10 degrees F. for 20 minutes, the injury was less in the hardier varieties, thus showing their ability better to withstand such a sudden drop in temperature. 15. While in the various lines of comparison which were made there were found many indications of morphological differences between hardy and tender varieties, yet from the practical view point as yet it is impossible to name anyone test by which the degree of constitutional hardiness of a seedling apple may be foretold. Among the various tests for hardiness, that of the length of season required by the tree to mature the season\u27s growth is of first importance. Perhaps by taking careful notes on a number of trees of any particular variety for two or three years or more, noting their time of starting and cessation of growth, their ability to produce a good root system from the cion, their water content, the resistance of their twigs to sudden zero temperatures, and their rate of evaporation, a pretty accurate idea of the ability of the tree to withstand, ,cold might be obtained. If in addition the variety has hard wood, a good amount of stored starch and large petals these would be further indications of hardiness, although from this study it appears that these points are of less importance than those first named

Subscale, hydrogen-burning, airframe-integrated-scramjet: Experimental and theoretical evaluation of a water cooled strut airframe-integrated-scramjet: Experimental leading edge

A water-cooled leading-edge design for an engine/airframe integrated scramjet model strut leading edge was evaluated. The cooling design employs a copper cooling tube brazed just downstream of the leading edge of a wedge-shaped strut which is constructed of oxygen-free copper. The survival of the strut leading edge during a series of tests at stagnation point heating rates confirms the practicality of the cooling design. A finite difference thermal model of the strut was also proven valid by the reasonable agreement of calculated and measured values of surface temperature and cooling-water heat transfer

Variational ground states of 2D antiferromagnets in the valence bond basis

We study a variational wave function for the ground state of the two-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. The expansion coefficients are products of amplitudes h(x,y) for valence bonds connecting spins separated by (x,y) lattice spacings. In contrast to previous studies, in which a functional form for h(x,y) was assumed, we here optimize all the amplitudes for lattices with up to 32*32 spins. We use two different schemes for optimizing the amplitudes; a Newton/conjugate-gradient method and a stochastic method which requires only the signs of the first derivatives of the energy. The latter method performs significantly better. The energy for large systems deviates by only approx. 0.06% from its exact value (calculated using unbiased quantum Monte Carlo simulations). The spin correlations are also well reproduced, falling approx. 2% below the exact ones at long distances. The amplitudes h(r) for valence bonds of long length r decay as 1/r^3. We also discuss some results for small frustrated lattices.Comment: v2: 8 pages, 5 figures, significantly expanded, new optimization method, improved result

Site dilution of quantum spins in the honeycomb lattice

We discuss the effect of site dilution on both the magnetization and the density of states of quantum spins in the honeycomb lattice, described by the antiferromagnetic Heisenberg spin-S model. For this purpose a real-space Bogoliubov-Valatin transformation is used. In this work we show that for the S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin S=1/2, however, the linear spin wave approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the Stochastic Series Expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo method: (i) a better value for the staggered magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. In the solution of the problem using linear the spin wave method we pay special attention to the presence of zero energy modes. Using a combination of linear spin wave analysis and the recursion method we were able to obtain the thermodynamic limit behavior of the density of states for both the square and the honeycomb lattices. We have used both the staggered magnetization and the density of states to analyze neutron scattering experiments and Neel temperature measurements on quasi-two- -dimensional honeycomb systems. Our results are in quantitative agreement with experimental results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.Comment: 21 pages (REVTEX), 16 figure