1,908 research outputs found
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, CFCHOCHF, CFCHClOCHF and CFCHOCClF, 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 + CFCHOCHF: = (2.00.8) 10 exp( – 2110 150 K / T) cm molecule s
OH + CFCHClOCHF: = (4.5 1.3) 10 exp( – 940 100 K / T) cm molecule s
OH + CFCHOCClF: = (1.6 0.6) 10 exp( – 1100 125 K / T) cm molecule s
Cl + CFCHOCHF: = (6.1 1.4) 10 exp( – 1830 90 K / T) cm molecule s
Cl + CFCHClOCHF: = (7.8 2.6) 10 exp( – 2980 130 K / T) cm molecule s
Cl + CFCHOCClF: = (2.2 0.2) 10 exp( – 2700 40 K / T) cm molecule s
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
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