arXiv subjects

Shiwei Zhang

Publications and source records attributed to Shiwei Zhang.

At least 235 records · Page 13Linked to original sources

arXiv2007

Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2

The use of an approximate reference state wave function |Phi_r> in electronic many-body methods can break the spin symmetry of Born-Oppenheimer spin-independent Hamiltonians. This can result in significant errors, especially when bonds are stretched or broken. A simple spin-projection method is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations, which yields spin-contamination-free results, even with a spin-contaminated |Phi_r>. The method is applied to the difficult F2 molecule, which is unbound within unrestricted Hartree-Fock (UHF). With a UHF |Phi_r>, spin contamination causes large systematic errors and long equilibration times in AFQMC in the intermediate, bond-breaking region. The spin-projection method eliminates these problems, and delivers an accurate potential energy curve from equilibrium to the dissociation limit using the UHF |Phi_r>. Realistic potential energy curves are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are in excellent agreement with experiment.

physics.comp-ph↗

arXiv2007

The Hartree-Fock ground state of the three-dimensional electron gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin density wave (SDW) instability. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the HF ground state of the 3D electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the SDW is smaller than $2 k_F$. The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.

cond-mat.str-el↗

arXiv2007

Finite-size correction in many-body electronic structure calculations

Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a modified local density approximation calculation. A parametrization for the FS exchange-correlation functional is obtained. The method is simple and gives post-processing corrections that can be applied to any MB results. Applications to a model insulator (P$_2$ in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.

cond-mat.mtrl-sci↗

arXiv2007

Bond breaking with auxiliary-field quantum Monte Carlo

Bond stretching mimics different levels of electron correlation and provides a challenging testbed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N$_2$, and in the H$_{50}$ chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N$_2$, we also study the use of multiple-determinant trial wave functions from multi-configuration self-consistent-field (MCSCF) calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.

physics.comp-ph↗

arXiv2007

A study of H+H$_2$ and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with planewave and Gaussian basis sets

We present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H$_2$ near the equilibrium geometry and in the van der Walls limit, as well as H$_2$O, OH, and H$_2$O$_2$ molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a planewave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.

physics.comp-ph↗

arXiv2007

Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules

The phaseless auxiliary-field quantum Monte Carlo (AF QMC) method [S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)] is used to carry out a systematic study of the dissociation and ionization energies of second-row group 3A-7A atoms and dimers, Al, Si, P, S, Cl. In addition, the P_2 dimer is compared to the third-row As_2 dimer, which is also triply-bonded. This method projects the many-body ground state by means of importance-sampled random walks in the space of Slater determinants. The Monte Carlo phase problem, due to the electron-electron Coulomb interaction, is controlled via the phaseless approximation, with a trial wave function |Psi_T>. As in previous calculations, a mean-field single Slater determinant is used as |Psi_T>. The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a planewave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the planewave AF QMC method are presented. The isolated systems chosen here allow a systematic study of the various algorithmic issues. We show the accuracy of the planewave method and discuss its convergence with respect to parameters such as the supercell size and planewave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.

cond-mat.mtrl-sci↗

arXiv2006

Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements

A series of calculations for the first- and second-row post-d elements (Ga-Br and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo (AF QMC) method. This method is formulated in a Hilbert space defined by any chosen one-particle basis, and maps the many-body problem into a linear combination of independent-particle solutions with external auxiliary fields. The phase/sign problem is handled approximately by the phaseless formalism using a trial wave function, which in our calculations was chosen to be the Hartree-Fock solution. We used the consistent correlated basis sets of Peterson and coworkers, which employ a small core relativistic pseudopotential. The AF QMC results are compared with experiment and with those from density-functional (GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total energies agree with CCSD(T) to within a few milli-hartrees across the systems and over several basis sets. The calculated atomic electron affinities, ionization energies, and spectroscopic properties of dimers are, at large basis sets, in excellent agreement with experiment.

physics.comp-ph↗

arXiv2006

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system size, as a low power. A QMC approach with auxiliary fields in principle allows an exact solution of the Schrodinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few milli-Hartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled-cluster with single and double excitations and with non-iterative triples, CCSD(T). For stretched bonds in H$_2$O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).

physics.comp-ph↗

arXiv2005

Auxiliary-field quantum Monte Carlo study of TiO and MnO molecules

Calculations of the binding energy of the transition metal oxide molecules TiO and MnO are presented, using a recently developed phaseless auxiliary field quantum Monte Carlo approach. This method maps the interacting many-body problem onto a linear combination of non-interacting problems by a complex Hubbard-Stratonovich transformation, and controls the phase/sign problem with a phaseless approximation relying on a trial wave function. It employs random walks in Slater determinant space to project the ground state of the system, and allows use of much of the same machinery as in standard density functional theory calculations, such as planewave basis and non-local pseudopotentials. The calculations used a single Slater determinant trial wave function obtained from a density functional calculation, with no further optimization. The calculated binding energies are in good agreement with experiment and with recent diffusion Monte Carlo results. Together with previous results for sp-bonded systems, the present study indicates that the phaseless auxiliary field method is a robust and promising approach for the study of correlation effects in real materials.

cond-mat.str-el↗

arXiv2005

Correlation effects in the ground state of trapped atomic Bose gases

We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calculate the ground state of the gas using a ground-state auxiliary-field quantum Monte Carlo (QMC) method [Phys. Rev. E 70, 056702 (2004)]. We examine the properties of the gas, such as the energetics, condensate fraction, real-space density, and momentum distribution, as a function of the number of particles and the scattering length. We find that the mean-field Gross-Pitaevskii (GP) approach gives qualitatively incorrect result of the kinetic energy as a function of the scattering length. We present detailed QMC data for the various quantities, and discuss the behavior of GP, modified GP, and the Bogoliubov method under a local density approximation.

cond-mat.other↗

arXiv2005

Accurate, efficient and simple forces with Quantum Monte Carlo methods

Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite. We obtain very accurate geometries for the molecules H$_2$, LiH, CH$_4$, NH$_3$, H$_2$O and HF, with a Slater-Jastrow trial wave function. Harmonic frequencies for diatomics are also in good agreement with experiment. An antithetical sampling method is also discussed for additional reduction of the variance.

physics.comp-ph↗

arXiv2004

Kinetic Monte Carlo Simulations of Crystal Growth in Ferroelectric Alloys

The growth rates and chemical ordering of ferroelectric alloys are studied with kinetic Monte Carlo (KMC) simulations using an electrostatic model with long-range Coulomb interactions, as a function of temperature, chemical composition, and substrate orientation. Crystal growth is characterized by thermodynamic processes involving adsorption and evaporation, with solid-on-solid restrictions and excluding diffusion. A KMC algorithm is formulated to simulate this model efficiently in the presence of long-range interactions. Simulations were carried out on Ba(Mg_{1/3}Nb_{2/3})O_3 (BMN) type materials. Compared to the simple rocksalt ordered structures, ordered BMN grows only at very low temperatures and only under finely tuned conditions. For materials with tetravalent compositions, such as (1-x)Ba(Mg_{1/3}Nb_{2/3})O_3 + xBaZrO_3 (BMN-BZ), the model does not incorporate tetravalent ions at low-temperature, exhibiting a phase-separated ground state instead. At higher temperatures, tetravalent ions can be incorporated, but the resulting crystals show no chemical ordering in the absence of diffusive mechanisms.

cond-mat.mtrl-sci↗

arXiv2004

Quantum Monte Carlo method for the ground state of many-boson systems

We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. The method is in principle exact. We illustrate this method with a trapped atomic boson gas, where the atoms interact via an attractive or repulsive contact two-body potential. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems, and arbitrarily-sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field calculations for trapped atoms, and discuss the close formal relation between our method and the GP approach. Our method provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of non-interacting solutions. We discuss various algorithmic issues, including importance sampling and the back-propagation technique for computing observables, and illustrate them with numerical studies. We show results for systems with up to N ~ 400 bosons.

physics.comp-ph↗

arXiv2002

Quantum Monte Carlo method using phase-free random walks with Slater determinants

We develop a quantum Monte Carlo method for many fermions that allows the use of any one-particle basis. It projects out the ground state by random walks in the space of Slater determinants. An approximate approach is formulated to control the phase problem with a trial wave function $|Ψ_T>$. Using plane-wave basis and non-local pseudopotentials, we apply the method to Si atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater determinant wave functions from density functional theory calculations were used as $|Ψ_T>$ with no additional optimization. The calculated binding energy of Si2 and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.

cond-mat↗

arXiv2001

Constrained-path quantum Monte Carlo simulations of the zero-temperature disordered two-dimensional Hubbard model

We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two dimensional, repulsive Hubbard model at T=0. A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, U < 2t in the case of bond disorder, and U < 4t in the case of on-site disorder. Using ground-state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For U=4t, we find a critical bond disorder of Vc = (1.6 +- 0.4)t even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of Vc = (5.0 +- 0.5)t at U=4t.

cond-mat.str-el↗

arXiv1999

Constrained Path Monte Carlo For Fermions

This article contains lecture notes on the constrained path Monte Carlo method and its applications to study the Hubbard model. The lectures were given at the NATO Advanced Summer Institute held in Ithaca NY (1998). The article is published as a chapter in the book `Quantum Monte Carlo Methods in Physics and Chemistry,' Ed. M.P. Nightingale and C.J. Umrigar (Kluwer Academic Publishers, 1999).

cond-mat↗

arXiv1999

Finite-Temperature Monte Carlo Calculations For Systems With Fermions

We present a quantum Monte Carlo method which allows calculations on many-fermion systems at finite temperatures without any sign decay. This enables simulations of the grand-canonical ensemble at large system sizes and low temperatures. Both diagonal and off-diagonal expectations can be computed straightforwardly. The sign decay is eliminated by a constraint on the fermion determinant. The algorithm is approximate. Tests on the Hubbard model show that accurate results on the energy and correlation functions can be obtained.

cond-mat↗

arXiv1999

Step-Bunching Transitions on Vicinal Surfaces and Quantum n-mers

We study vicinal crystal surfaces within the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of phases in which steps coalesce into bunches of $n_b$ steps each. The value of $n_b$ varies with temperature and the ratio of short to long range interaction strengths. For bunches with large number of steps, we show that, at T=0, our bunch phases correspond to the well known periodic groove structure first predicted by Marchenko. An extension to $T>0$ is developed. We propose that the bunch phases have been observed in very recent experiments on Si surfaces, and further experiments are suggested. Within the context of a mapping of the model to a system of bosons on a 1D lattice, the bunch phases appear as quantum n-mers.

cond-mat.soft↗