Showing papers on "Quantum Monte Carlo published in 2009"
TL;DR: In this article, the structure of the Stone-Wales defect in graphene is more complex than hitherto appreciated, rather than being a simple in-plane transformation of two carbon atoms, out-of-plane defect structures that extend over several nanometers are predicted.
Abstract: Density functional theory and quantum Monte Carlo simulations reveal that the structure of the Stone-Wales (SW) defect in graphene is more complex than hitherto appreciated. Rather than being a simple in-plane transformation of two carbon atoms, out-of-plane wavelike defect structures that extend over several nanometers are predicted. Equivalent wavelike SW reconstructions are predicted for hexagonal boron-nitride and polycyclic aromatic hydrocarbons above a critical size, demonstrating the relevance of these predictions to $s{p}^{2}$-bonded materials in general.
442 citations
TL;DR: The field of continuum and discrete Frohlich polaron (bi) polarons has been studied extensively in the literature starting with the basics and covering a number of active directions of research as mentioned in this paper.
Abstract: It is remarkable how the Frohlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ~1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalization (ED) and quantum Monte Carlo (QMC) techniques. This paper reviews recent developments in the field of continuum and discrete (lattice) Frohlich (bi)polarons starting with the basics and covering a number of active directions of research.
317 citations
TL;DR: The field of continuum and discrete Froehlich polaron (bi)polarons has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques as mentioned in this paper.
Abstract: It is remarkable how the Froehlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article reviews recent developments in the field of continuum and discrete (lattice) Froehlich (bi)polarons starting with the basics and covering a number of active directions of research.
306 citations
TL;DR: The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models and discuss the advantages and limitations of these methods.
284 citations
TL;DR: In this paper, the authors present an approach that combines the local density approximation (LDA) and the dynamical mean field theory (DMFT) in the framework of the full-potential linear augmented plane-wave method.
Abstract: We present an approach that combines the local-density approximation (LDA) and the dynamical mean-field theory (DMFT) in the framework of the full-potential linear augmented plane-wave method. Wannier-type functions for the correlated shell are constructed by projecting local orbitals onto a set of Bloch eigenstates located within a certain energy window. The screened Coulomb interaction and Hund's coupling are calculated from a first-principles constrained random-phase approximation scheme. We apply this $\text{LDA}+\text{DMFT}$ implementation, in conjunction with a continuous-time quantum Monte Carlo algorithm, to the study of electronic correlations in LaFeAsO. Our findings support the physical picture of a metal with intermediate correlations. The average value of the mass renormalization of the $\text{Fe}\text{ }3d$ bands is about 1.6, in reasonable agreement with the picture inferred from photoemission experiments. The discrepancies between different $\text{LDA}+\text{DMFT}$ calculations (all technically correct) which have been reported in the literature are shown to have two causes: (i) the specific value of the interaction parameters used in these calculations and (ii) the degree of localization of the Wannier orbitals chosen to represent the $\text{Fe}\text{ }3d$ states, to which many-body terms are applied. The latter is a fundamental issue in the application of many-body calculations, such as DMFT, in a realistic setting. We provide strong evidence that the DMFT approximation is more accurate and more straightforward to implement when well-localized orbitals are constructed from a large energy window encompassing $\text{Fe-}3d$, $\text{As-}4p$, and $\text{O-}2p$ and point out several difficulties associated with the use of extended Wannier functions associated with the low-energy iron bands. Some of these issues have important physical consequences regarding, in particular, the sensitivity to the Hund's coupling.
265 citations
TL;DR: The interlayer bonding properties of graphite are computed using an ab initio many-body theory and an equilibrium interlayer binding energy is found in good agreement with most recent experiments.
Abstract: We compute the interlayer bonding properties of graphite using an ab initio many-body theory. We carry out variational and diffusion quantum Monte Carlo calculations and find an equilibrium interlayer binding energy in good agreement with most recent experiments. We also analyze the behavior of the total energy as a function of interlayer separation at large distances comparing the results with the predictions of the random phase approximation.
260 citations
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TL;DR: In this article, an introduction to the Monte Carlo method is given and concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained.
Abstract: Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained. The Monte Carlo method is illustrated by numerically studying the critical behavior of the two-dimensional Ising ferromagnet using finite-size scaling methods. In addition, advanced Monte Carlo methods are described (e.g., the Wolff cluster algorithm and parallel tempering Monte Carlo) and illustrated with nontrivial models from the physics of glassy systems. Finally, we outline an approach to study rare events using a Monte Carlo sampling with a guiding function.
255 citations
TL;DR: In this paper, the authors generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations.
Abstract: We generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations. Both weak-coupling and strong-coupling based methods are introduced, analyzed, and applied to the study of transport and relaxation dynamics in interacting quantum dots.
237 citations
TL;DR: In this paper, a numerically exact approach to nonequilibrium real-time dynamics that is applicable to quantum impurity models coupled to biased noninteracting leads, such as those relevant to quantum transport in nanoscale devices, is proposed.
Abstract: We propose a numerically exact approach to nonequilibrium real-time dynamics that is applicable to quantum impurity models coupled to biased noninteracting leads, such as those relevant to quantum transport in nanoscale devices. The method is based on a diagrammatic Monte Carlo sampling of the real-time perturbation theory along the Keldysh contour. We benchmark the method on a noninteracting resonant-level model and, as a first nontrivial application, we study zero-temperature nonequilibrium transport through a vibrating molecule.
156 citations
TL;DR: QWalk, a new computational package capable of performing quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons, is described.
155 citations
TL;DR: In this paper, the auxiliary field diffusion Monte Carlo (AFDMC) method combined with a fixed-phase approximation was used to calculate the energy of neutrons at zero temperature, and the effect of truncation of the simulation box was checked by employing the twist-averaged boundary conditions.
Abstract: We calculated the equation of state of neutron matter at zero temperature by means of the auxiliary field diffusion Monte Carlo (AFDMC) method combined with a fixed-phase approximation. The calculation of the energy was carried out by simulating up to 114 neutrons in a periodic box. Special attention was given to reducing finite-size effects at the energy evaluation by adding to the interaction the effect due to the truncation of the simulation box, and by performing several simulations using different numbers of neutrons. The finite-size effects due to kinetic energy were also checked by employing the twist-averaged boundary conditions. We considered a realistic nuclear Hamiltonian containing modern two- and three-body interactions of the Argonne and Urbana family. The equation of state can be used to compare and calibrate other many-body calculations and to predict properties of neutron stars.
TL;DR: A thorough comparative investigation of the excitation energies of the anionic and neutral forms of the green fluorescent protein (GFP) chromophore in the gas phase using a variety of first-principle theoretical approaches commonly used to access excited state properties of photoactive molecules finds that all approaches give roughly the same vertical excitation, while TDDFT predicts an excitation for the neutral Chromophore significantly lower than the highly correlated methods.
Abstract: We perform a thorough comparative investigation of the excitation energies of the anionic and neutral forms of the green fluorescent protein (GFP) chromophore in the gas phase using a variety of first-principle theoretical approaches commonly used to access excited state properties of photoactive molecules. These include time-dependent density functional theory (TDDFT), complete-active-space second-order perturbation theory (CASPT2), equation-of-motion coupled cluster (EOM-CC), and quantum Monte Carlo (QMC) methods. We find that all approaches give roughly the same vertical excitation for the anionic form, while TDDFT predicts an excitation for the neutral chromophore significantly lower than the highly correlated methods. Our findings support the picture emerging from the extrapolation of the Kamlet-Taft fit of absorption experimental data in solution and indicate that the protein gives rise to a considerable bathochromic shift with respect to vacuum. These results also open some questions on the interpretation of photodestruction spectroscopy experiments in the gas phase as well as on the accuracy of previous theoretical calculations in the more complex protein environment
TL;DR: In this paper, a Monte Carlo sampling based on collective atomic moves (wave moves) was introduced to access the long-wavelength limit for finite-size systems (up to 40 000 atoms) and they found a power-law behavior G(q)α q(-2+eta) with the same exponent eta approximate to 0.85 for both potentials.
Abstract: Structure and thermodynamics of crystalline membranes are characterized by the long-wavelength behavior of the normal-normal correlation function G(q). We calculate G(q) by Monte Carlo and molecular dynamics simulations for a quasiharmonic model potential and for a realistic potential for graphene. To access the long-wavelength limit for finite-size systems (up to 40 000 atoms) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behavior G(q)alpha q(-2+eta) with the same exponent eta approximate to 0.85 for both potentials. This finding supports, from the microscopic side, the adequacy of the scaling theory of membranes in the continuum medium approach, even for an extremely rigid material such as graphene.
TL;DR: A particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models, is introduced.
Abstract: We introduce a particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models. The method enables Monte Carlo simulations in arbitrary ensembles and direct calculation of free energies. We present results for the phase diagram and the critical point of a binary homopolymer blend. For a symmetric diblock copolymer, we compute the distribution of local stress in lamellae and locate the order-disorder transition.
TL;DR: In this article, a combination of finite-temperature density matrix renormalization group simulations and time-series prediction is proposed for spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures.
Abstract: We present time-dependent density matrix renormalization group simulations $(t\text{-DMRG})$ at finite temperatures. It is demonstrated how a combination of finite-temperature $t\text{-DMRG}$ and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures. This is illustrated with spin structure factors of $XX$ and $XXX$ spin-$\frac{1}{2}$ chains. For the $XX$ model we can compare against an exact solution, and for the $XXX$ model (Heisenberg antiferromagnet) against a Bethe ansatz solution and quantum Monte Carlo data.
TL;DR: In this article, large scale determinant quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling are presented.
Abstract: We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the noninteracting limit is significantly broadened by the electronic correlations but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite-size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the Green’s function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments.
TL;DR: In this paper, the physical principles and approximations employed in Monte Carlo simulations of coupled electron-photon transport are reviewed and a brief analysis of the assumptions underlying the trajectory picture used to generate random particle histories is presented.
Abstract: The physical principles and approximations employed in Monte Carlo simulations of coupled electron–photon transport are reviewed. After a brief analysis of the assumptions underlying the trajectory picture used to generate random particle histories, we concentrate on the physics of the various interaction processes of photons and electrons. For each of these processes we describe the theoretical models and approximations that lead to the differential cross sections employed in general-purpose Monte Carlo codes. References to relevant publications and data resources are also provided.
TL;DR: Analytical and numerical evidence is presented that, driven by the same quantum fluctuations, this first order transition is preempted by the formation of an inhomogeneous magnetic phase in the Fulde-Ferrel-Larkin-Ovchinnikov state.
Abstract: A variety of analytical techniques suggest that quantum fluctuations lead to a fundamental instability of the Fermi liquid that drives ferromagnetic transitions first order at low temperatures. We present both analytical and numerical evidence that, driven by the same quantum fluctuations, this first order transition is preempted by the formation of an inhomogeneous magnetic phase. This occurs in a manner that is closely analogous to the formation of the inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We derive these results from a field-theoretical approach supplemented with numerical quantum Monte Carlo simulations.
TL;DR: A program suite for simulating Quantum Chromodynamics on a 4-dimensional space–time lattice with basic Hybrid Monte Carlo algorithm is discussed and a number of algorithmic improvements are explained.
TL;DR: A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-Ohmic spin-boson model and the discrepancy with recent renormalization group predictions is traced back to the effect of a dangerously irrelevant variable.
Abstract: A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-Ohmic spin-boson model. When the power s of the spectral function Jomega proportional, variant omegas is smaller than 1/2, the critical exponents are found to be classical, mean-field like. Potential sources for the discrepancy with recent renormalization group predictions are traced back to the effect of a dangerously irrelevant variable.
TL;DR: Two quantum Monte Carlo schemes are introduced that allow the computation of fidelity and its susceptibility for large interacting many-body systems and a scaling theory is developed which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length.
Abstract: When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
TL;DR: A method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor is introduced.
Abstract: We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant nondynamical correlations are correctly reproduced once an appropriate number n of molecular orbitals is considered. The value of n is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be(2), B(2), C(2), N(2), O(2), and F(2)) and heteronuclear (LiF and CN) dimers for which strong nondynamical correlations and/or weak van der Waals interactions are present.
TL;DR: It is shown that Wang-Landau sampling, combined with suitable Monte Carlo trial moves, provides a powerful method for both the ground state search and the determination of the density of states for the hydrophobic-polar protein model and the interacting self-avoiding walk model for homopolymers.
Abstract: We show that Wang-Landau sampling, combined with suitable Monte Carlo trial moves, provides a powerful method for both the ground state search and the determination of the density of states for the hydrophobic-polar (HP) protein model and the interacting self-avoiding walk (ISAW) model for homopolymers. We obtain accurate estimates of thermodynamic quantities for HP sequences with >100 monomers and for ISAWs up to >500 monomers. Our procedure possesses an intrinsic simplicity and overcomes the limitations inherent in more tailored approaches making it interesting for a broad range of protein and polymer models.
TL;DR: Numerical estimates for a new ansatz for the ground-state wave function of quantum many-body systems on a lattice are in quite good agreement with exact ones for unfrustrated systems, and compare favorably to other methods for frustrated ones.
Abstract: We propose a new ansatz for the ground-state wave function of quantum many-body systems on a lattice. The key idea is to cover the lattice with plaquettes and obtain a state whose configurational weights can be optimized by means of a variational Monte Carlo algorithm. Such a scheme applies to any dimension, without any 'sign' instability. We show results for various two-dimensional spin models (including frustrated ones). A detailed comparison with available exact results, as well as with variational methods based on different ansatze, is offered. In particular, our numerical estimates are in quite good agreement with exact ones for unfrustrated systems, and compare favorably to other methods for frustrated ones.
TL;DR: An efficient Monte Carlo algorithm is developed that generates thousands of probable solutions from which the statistical properties of the solution can be analyzed and it is found that although all of the individual solutions are spiky, the mean solution spectrum is smooth and similar to the regularized solution.
TL;DR: The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment, but single-determinant wave functions do not yield accurate DMC energies of the states of (1)A(1) symmetry, indicating that it is important to include in the wave function Slater determinants that describe static (strong) correlation.
Abstract: The ground and lowest three adiabatic excited states of methylene are computed using the variational Monte Carlo and diffusion Monte Carlo (DMC) methods using progressively larger Jastrow–Slater multideterminant complete active space (CAS) wave functions. The highest of these states has the same symmetry, A11, as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment, but single-determinant wave functions do not yield accurate DMC energies of the states of A11 symmetry, indicating that it is important to include in the wave function Slater determinants that describe static (strong) correlation. Excitation energies obtained using recently proposed pseudopotentials [Burkatzki et al., J. Chem. Phys. 126, 234105 (2007)] differ from the all-electron excitation energies by at most 0.04 eV.
TL;DR: It is demonstrated that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques and the critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results.
Abstract: We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical N\'eel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.
TL;DR: Given the relative paucity of QMC reports for noncovalent interactions, it is interesting to see that QMC and coupled cluster with single, double, and perturbative triple excitations are in very good agreement for most of the binding energy curve, although at short distances there are small deviations on the order of 20 meV.
Abstract: Weak noncovalent interactions such as van der Waals and hydrogen bonding are ubiquitous in nature, yet their accurate description with electronic structure theories is challenging. Here we assess the ability of a variety of theories to describe a water-benzene binding energy curve. Specifically, we test Hartree-Fock, second-order Moller-Plesset perturbation theory, coupled cluster, density functional theory with several exchange-correlation functionals with and without empirical vdW corrections, and quantum Monte Carlo (QMC). Given the relative paucity of QMC reports for noncovalent interactions, it is interesting to see that QMC and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are in very good agreement for most of the binding energy curve, although at short distances there are small deviations on the order of 20 meV.
TL;DR: The quantum Monte Carlo (QMC) method has become increasingly important for solution of the stationary Schrodinger equation for atoms, molecules and solids as mentioned in this paper, and has been shown to exhibit high accuracy that scales better with system size than other ab initio methods.
TL;DR: In this article, the authors used the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to study excited states, providing an alternative to standard quantum chemistry methods.
Abstract: We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M3-M4 with system size M, has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging C2 molecule as a test case, we calculate the potential energy curves of the ground and two low-lying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configuration-interaction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.