Showing papers on "Quantum Monte Carlo published in 1982"
TL;DR: In this article, the ground state energies of H2, LiH, Li2, and H2O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail.
Abstract: The ground‐state energies of H2, LiH, Li2, and H2O are calculated by a fixed‐node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions ΨT are chosen. Each ΨT consists of a single Slater determinant of molecular orbitals multiplied by a product of pair‐correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schrodinger equation by treating it as a diffusion equation. In this approach, ΨT serves as a ‘‘guiding function’’ for a random walk of the electrons through configuration space. In the fixed‐node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of ΨT. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The e...
893 citations
TL;DR: In this paper, a Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored, and it is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems.
Abstract: A Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored. It is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems, where the number of discrete points must be large. A new energy estimator based on the virial theorem is proposed and shown to be well behaved. The main points of the paper are illustrated, using the harmonic oscillator as an example.
422 citations
TL;DR: In this article, a quenched version of the Eguchi-Kawai model is proposed, which gives good behavior at weak couplings, based on an analytic investigation and on Monte Carlo simulations.
337 citations
TL;DR: In this paper, a direct-space, imaginary-time representation of the fermion field is proposed for numerical simulations of one-dimensional systems with fermions and boson degrees of freedom.
Abstract: We discuss a new method to perform numerical simulations of one-dimensional systems with fermion and boson degrees of freedom. The method is based on a direct-space, imaginary-time representation of the fermion field. It is fast so that systems having up to 100 sites can easily be simulated. In addition, the method provides an intuitive physical "picture" of the ground state of a one-dimensional many-body system. We discuss in detail how to implement the method and how to compute various physical quantities. In particular, we show how to extend the method to study averages of off-diagonal quantities in an occupation-number representation. To assess the accuracy of our procedure, we apply it to free fermions in one dimension and compare with exact results. We then study a model of spinless interacting fermions and obtain the expected phase structure and behavior of correlation functions. We also consider the extended Hubbard model at various points in its phase diagram and study the behavior of spin-density, charge-density, and pairing correlation functions. We then study the Gross-Neveu model and show how the behavior depends on the number of fermion flavors. Finally, we consider an electron-phonon model and study its behavior both in the one-particle polaron sector and in the half-filled-band case. Along the way we show pictures of the ground-state configurations that give physical insight into the properties of the systems, like charge-density-wave, spin-density-wave, and superconducting states, "fractional charges," and solitons. We conclude by comparing our method with other methods and discuss the possibility of extending it to higher dimensions.
298 citations
TL;DR: In this article, the authors derived exact statistical mechanical relations for polyelectrolyte systems within the primitive model using the cell model and determined the osmotic pressure through an explicit evaluation of the derivative of the partition function.
Abstract: Some exact statistical mechanical relations have been derived for polyelectrolyte systems within the primitive model. Using the cell model, the osmotic pressure is determined through an explicit evaluation of the derivative of the partition function. Planar, cylindrical, and spherical systems are considered and for a planar charged wall the contact value theorem [Henderson and Blum, J. Chem. Phys. 69, 5441 (1978)] is obtained as a special case. Analogous relations are derived for the cylindrical and spherical geometries. It is argued that the exact relations can be used as consistency tests for analytical approximations. It is pointed out that one merit of the Poisson–Boltzmann approximation is that the validity of the exact equations is retained. Finally, a simple method is devised for determining the osmotic pressure from Monte Carlo simulations. Results from such simulations are used to assess the accuracy of the osmotic pressure calculated using the Poisson–Boltzmann equation. For monovalent ions, the pressure is overestimated by 10%–50% in the cases studied, while with divalent counterions the error is substantially larger and a discrepancy of one order of magnitude is found.
282 citations
TL;DR: In this article, an improved Monte Carlo method is presented for lattice gauge theories with fermions, taking the pion mass and meson Regge trajectory slope as input, this procedure is used to calculate the rho mass on lattices up to 12 4 for gauge group¯I, the best discrete approximation to SU(2).
150 citations
TL;DR: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported in this article.
Abstract: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported. Thermodynamic properties were studied with use of the constant-pressure Monte Carlo method; Widom's particle-insertion method was used to measure the chemical potential. The phase diagram is found to differ considerably from predictions of a second-virial ("Onsager") theory. Virial coefficients up to the fifth were computed; b5 is found to be negative.
133 citations
TL;DR: In this paper, a general procedure was described that put the practice of integral equation theory for molecular fluids on a par with that of simple fluids: any integral equation approximation can be solved for any intermolecular potential with no additional approximations beyond those inherent in numerical analysis.
Abstract: A general procedure is described that puts the practice of integral equation theory for molecular fluids on a par with that of simple fluids: any integral equation approximation can be solved for any intermolecular potential with no additional approximations beyond those inherent in numerical analysis. The essential elements are expansions in spherical harmonics and numerical evaluation of the spherical harmonic coefficients of the pair distribution function. An explicit formula is derived giving the Helmholtz free energy from the computed coefficients.
91 citations
TL;DR: In this paper, the GFMC method was used to obtain the lowest energy state of the ground state of a few-body system, which was shown to be computationally feasible for several-body systems.
Abstract: The Green’s function Monte Carlo method used for obtaining exact solutions to the Schrodinger equation of boson systems is generalized to treat systems of several fermions. We show that when it is possible to select eigenfunctions of the Hamiltonian based on physical symmetries, the GFMC method can be used to yield the lowest energy state of that symmetry. In particular, the lowest totally antisymmetric eigenfunction, the fermion ground state, can be obtained. Calculations on several two‐ and three‐body model problems show the method to be computationally feasible for few‐body systems.
89 citations
TL;DR: By the use of umbrella sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard-Jones liquid mixtures.
Abstract: By the use of umbrella‐sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard‐Jones liquid mixtures. The variational method in perturbation theory is found to account for these Monte Carlo data. Validity of some representative semiempirical theories is discussed and it is found that none of them can reproduce the present Monte Carlo results reasonably well. Finally the phase stability of the present models is discussed in terms of both the free energy of mixing and local composition values recently obtained from our molecular dynamics calculations.
85 citations
TL;DR: In this paper, the stability of the topological charge fluctuation in SU(2) is checked against some variations of its lattice definition by subtracting a partly computed perturbative tail to Monte Carlo data.
TL;DR: In this article, the effect of quantum fluctuations of the phonon field on the ground state character of one-dimensional electron-phonon systems was studied with a numerical simulation technique.
Abstract: The effect of quantum fluctuations of the phonon field on the ground-state character of one-dimensional electron-phonon systems is studied with a numerical simulation technique. Two different electron-phonon models are studied, both for spinless and spin-\textonehalf{} electrons, in the half-filled-band case. In both models, it is found that in the spinless case quantum fluctuations destroy the long-range dimerization order for small electron-phonon coupling constant $\ensuremath{\lambda}$. For the spin-\textonehalf{} case, the results are consistent with the Peierls transition occurring at $\ensuremath{\lambda}=0$.
TL;DR: In this paper, the mean field estimates of the transition temperature and discontinuity of the order parameter are in good agreement with computer simulations for N = 3 and 4, and the N → ∞ limit of mean field theory has a first-order phase transition.
TL;DR: In this article, the phase diagram of the two-dimensional, three-state chiral Potts or asymmetric clock model is studied using Monte Carlo techniques. And the phase boundaries are compared to those obtained using the finite-size renormalization group and the free fermion approximation.
Abstract: The phase diagram of the two-dimensional, three-state chiral Potts or asymmetric clock model is studied using Monte Carlo techniques. The phase boundaries are compared to those obtained using the finite-size renormalization group and the free fermion approximation. The incommensurate phase is described in detail and crossover effects near the Lifshitz point are discussed.
TL;DR: In this paper, the mass gap in SU(2) lattice gauge theory was computed by combining Monte Carlo and variational techniques, and the estimate m g = (2.4 ± 0.6) K, K being the string tension.
TL;DR: In this paper, the energy density of the pure SU(3) Yang-Mills system was determined by Monte Carlo simulation, and the Stefan-Boltzmann law was satisfied within errors.
TL;DR: In this article, Monte Carlo simulations of dislocation vector systems with long-range interactions reveal two possible types of phase transitions depending on the core energy of dislocations, and the Kosterlitz-Thouless theory agrees well with the simulation results.
Abstract: Monte Carlo simulations of dislocation vector systems with long-range interactions reveal two possible types of phase transitions depending on the core energy of dislocations. For dislocations with a large core energy the melting transition is found to be continuous and due to dislocation unbinding. The Kosterlitz-Thouless theory agrees well with the simulation results. For a small core energy the melting transition is caused by the nucleation of grain boundary loops and is found to be first order. The latter transition may correspond to the previous computer experiments on various atomic systems. In addition to thermodynamic quantities such as the energy and specific heat, microscopic configurations and orientational correlation functions are also calculated.
TL;DR: In this article, the first quantitative evidence of critical quantum fluctuations and superlocalization of the small polaron model in one, two, and three dimensions is presented, starting from a discrete version of the Feynman pathintegral representation of the partition function, the boson field is eliminated analytically and the polaron contribution is calculated by the standard Monte Carlo Method.
Abstract: The first quantitative evidence of critical quantum fluctuations and superlocalization of the small polaron model in one, two, and three dimensions is presented. Starting from a discrete version of the Feynman path-integral representation of the partition function, the boson field is eliminated analytically and the polaron contribution is calculated by means of the standard Monte Carlo Method.
TL;DR: In this paper, an exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described, for both one-dimensional and three-dimensional ferromagnetic and antiferromagnetic systems.
Abstract: An exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described. Results for one-dimensional ferromagnetic and antiferromagnetic systems and for three-dimensional ferromagnetic systems show that the method can be used to study quantum spin systems as extensively as classical spin systems are studied with conventional Monte Carlo methods.
TL;DR: In this article, the energy density and pressure of the SU(3) Yang-Mills system (gluon matter) were calculated by Monte Carlo simulations on lattice.
TL;DR: In this paper, a Monte Carlo model is used to simulate the thermodynamic equilibrium of a substitutional binary f.c. solid solution with pairwise interactions, which is used for the determination of ground state structures, the calculation of short-range and long-range order data at non-zero temperatures, and the computation of the uppermost ordering temperatures.
TL;DR: In this article, a real space renormalization group is formulated for percolation of overlapping discs with a variety of distributions of disc radii and the Monte Carlo method is used for obtaining recursion relations.
Abstract: A real space renormalization group is formulated for continuum (off-lattice) percolation problems It is applied to the system of overlapping discs with a variety of distributions of disc radii Monte Carlo method is used for obtaining recursion relations The results support universality: The Harris criterion seems to work for percolation The position of the critical point shows stability against introducing a distribution in the disc radii
TL;DR: In this article, a multispin coding technique was applied to the kinetic Ising model with size 600*600*600 and the magnetization was found to decay asymptotically as exp(-t/2.90) ift is measured in Monte Carlo steps per spin, and M(t = 0) = 1 initially.
Abstract: Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetizationM atT=1.4*T
c is found to decay asymptotically as exp(-t/2.90) ift is measured in Monte Carlo steps per spin, and M(t = 0) = 1 initially.
TL;DR: In this article, the dynamic Monte Carlo renormalization group is applied to the two-dimensional Kawasaki and three-dimensional Glauber models and the best matching results for the Kawasaki model yield a value of 3.80$ for the dynamical exponent, as compared with the exact value $z=3.75$.
Abstract: The dynamic Monte Carlo renormalization group is applied to the two-dimensional Kawasaki and three-dimensional Glauber models. Our best "matching" results for the Kawasaki model yield a value of $z=3.80$ for the dynamical exponent, as compared with the exact value $z=3.75$. This provides strong confirmation for the validity of this method. The results for the Glauber model are less accurate, but our estimate of $z\ensuremath{\simeq}2.08$ is in reasonable agreement with the $\ensuremath{\epsilon}$ expansion.
TL;DR: In this article, a phenomenological renormalization method for analyzing Monte Carlo data in the critical region is proposed, illustrated by an analysis of the structure factor of the two-dimensional axial next-nearest neighbor Ising model.
Abstract: A method, akin to phenomenological renormalisation, for analysing Monte Carlo data in the critical region is proposed. The method is illustrated by an analysis of the structure factor of the two-dimensional axial next-nearest neighbour Ising model.
TL;DR: In this paper, the SU(3) gluon condensate was determined from a fit to the Creutz ratios of Wilson loop expectation values taken from new Monte Carlo data.