No abstract

We develop a quantum Monte Carlo method for many fermions that allows the use of any oneparticle 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 |ΨT . 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 |ΨT 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.PACS numbers: 02.70. Ss, Quantum Monte Carlo (QMC) methods based on auxiliary fields (AF) are used in areas spanning condensed matter physics, nuclear physics, and quantum chemistry. These methods [1,2] allow essentially exact calculations of ground-state and finite-temperature equilibrium properties of interacting many fermion systems. The required CPU time scales in principle as a power law with system size, and the methods have been applied to study a variety of problems including the Hubbard model, nuclear shell models, and molecular electronic structure. The central idea of these methods is to write the imaginarytime propagator of a many-body system with two-body interactions in terms of propagators for independent particles interacting with external auxiliary fields. The independent particle problems are solved for configurations of the AF and averaging over different AF configurations is then performed by Monte Carlo (MC) techniques.QMC methods with auxiliary fields have several appealing features. For example, they allow one to choose any one-particle basis suitable for the problem, and to fully take advantage of well-established techniques to treat independent particles. Given the remarkable development and success of the latter [3], it is clearly very desirable to have a QMC method that can use exactly the same machinery and systematically include correlation effects by simply building stochastic ensembles of the independent particle solutions. Vigorous attempts have been made from several fields to explore this possibility [4,5,6,7].A significant hurdle exists, however: except for special cases (e.g., Hubbard), the two-body interactions will require auxiliary fields that are complex . As a result, the single-particle orbitals become complex, and the MC averaging over AF configurations becomes an integration over complex variables in many dimensions. A phase problem thus occurs which ultimately defeats the algebraic scaling of MC and makes the method scale exponentially. This is analogous to but more severe than the fermion sign problem with real AF [8,9] or in real-space methods [10]. No satisfactory, general approach exists to control the phase problem. As a result, only small systems or special forms of interactions can be treated.In this paper we address this problem. W...

No abstract

No abstract

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 Schrödinger 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 H2O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).

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 (P2 in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.PACS numbers: 02.70. Ss, 71.15.Nc, Realistic many-body (MB) calculations for extended systems are needed to accurately treat systems where the otherwise successful density functional theory (DFT) approach fails. Examples range from strongly correlated materials, such as high-temperature superconductors, to systems with moderate correlation, for instance where accurate treatments of bond-stretching or bond-breaking are required. DFT or Hartree Fock (HF), which are effectively independent-particle methods, routinely exploit Bloch's theorem in calculations for extended systems. In crystalline materials, the cost of the calculations depends only on the number of atoms in the periodic cell, and the macroscopic limit is achieved by a quadrature in the Brillouin zone, using a finite number of k-points. MB methods, by contrast, cannot avail themselves of this simplification. Instead calculations must be performed using increasingly larger simulation cells (supercells). Because the Coulomb interactions are long-ranged, finite-size (FS) effects tend to persist to large system sizes, making reliable extrapolations impractical. The resulting FS errors in state-of-the-art MB quantum simulations often can be more significant than statistical and other systematic errors. Reducing FS errors is thus a key to broader applications of MB methods in real materials, and the subject has drawn considerable attention [1,2].In this paper, we introduce an external correction method, which is designed to approximately include FS corrections in modified DFT calculations with finite-size functionals. The method is simple, and provides postprocessing corrections applicable to any previously obtained MB results. Conceptually, it gives a consistent framework for relating FS effects in MB and DFT calculations, which is important if the two methods are to be seamlessly interfaced to bridge length scales. The correction method is applied to a model insulator (P 2 in a supercell), to semiconducting bulk Si, and to Na metal. We find that it consistently removes most of the FS errors, leading to rapid convergence of the MB results to the infinite system.We write the N -electron MB Hamiltonian in a supercell as (Rydberg atomic units are used throughout):where the ionic potential on i can be local or non-local, and r i is an electron position. The Coulomb interaction V FS between electrons depends on the supercell size and shape, due to modificatio...

No abstract

No abstract