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

Global Implications of U.S. Biofuels Policies in an Integrated Partial and General Equilibrium Framework

With the increasing research interests in biofuels, global implications of biofuels production have been generally examined either in a partial equilibrium (PE) or general equilibrium (GE) frameworks. Though both of these approaches have unique strengths, they also suffer from many limitations due to complexity of addressing all the relevant aspects of biofuels. In this paper we have exploited the strengths of both PE and GE approaches for analyzing the economic and environmental implications of the U.S. policies on corn-ethanol and biodiesel production. In this study, we utilize the Forest and Agricultural Sector Optimization Model (FASOMGHG: Adams et al. 1996, 2005; Beach et al. 2009), a non-linear programming, PE model for the United States. We also use the GTAP-BIO model (Birur et al. 2008), a multi-region, multi-sector CGE model for global-scale assessment of biofuels policies. Following Britz and Hertel (2009), we link the GTAP-BIO model through a static, quadratic restricted revenue function obtained from perturbing crop prices from the FASOMGHG model. With this linkage we implement the U.S. Corn ethanol and biodiesel scenarios in the GTAP-BIO model and obtain the FASOMGHG-consistent, global land use changes. The resulting crop price changes from the GE model are fed back into the FASOMGHG model to obtain the disaggregated impacts in the U.S.Biofuels, Indirect land use change, Land use emissions, Partial Equilibrium, Computable General Equilibrium, Land Economics/Use, Resource /Energy Economics and Policy,

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

Conductance through Quantum Dots Studied by Finite Temperature DMRG

With the Finite temperature Density Matrix Renormalization Group method (FT-DMRG), we depeloped a method to calculate thermo-dynamical quantities and the conductance of a quantum dot system. Conductance is written by the local density of states on the dot. The density of states is calculated with the numerical analytic continuation from the thermal Green's function which is obtained directly from the FT-DMRG. Typical Kondo behaviors in the quantum dot system are observed conveniently by comparing the conductance with the magnetic and charge susceptibilities: Coulomb oscillation peaks and the unitarity limit. We discuss advantage of this method compared with others.Comment: 14 pages, 13 fiure