Description of a solid using quantum Monte Carlo methods.

The fixed-node diffusion quantum Monte Carlo (DMC) method is the most accurate method known for calculating the energies of large many-particle quantum systems. The key element of the method is the development of accurate trial many-body wavefunctions which control the statistical efficiency of the calculations and the accuracy obtained. Accurate wavefunctions can be obtained by building correlation effects on top of mean field descriptions such as density functional theory. The wavefunctions can be improved by introducing multi-determinants, pairing functions, and backflow transformations. The calculations are expensive, but the method scales well with system size and calculations on 1000 particles are possible. Some recent applications of the DMC method to atoms, molecules and solids will be presented.The fixed-node diffusion quantum Monte Carlo (DMC) method is the most accurate method known for calculating the energies of large many-particle quantum systems. The key element of the method is the development of accurate trial many-body wavefunctions which control the statistical efficiency of the calculations and the accuracy obtained. Accurate wavefunctions can be obtained by building correlation effects on top of mean field descriptions such as density functional theory. The wavefunctions can be improved by introducing multi-determinants, pairing functions, and backflow transformations. The calculations are expensive, but the method scales well with system size and calculations on 1000 particles are possible. Some recent applications of the DMC method to atoms, molecules and solids will be presented.

Journal of Physics Condensed MatterJan 24, 20081 citation

QUANTUM MONTE CARLO FOR REALISTIC AND MODEL SOLIDS

Paola Gori‐Giorgi, ALESSANDRO FEDERICO, Giovanni B. Bachelet

Recent advances in computationalFeb 1, 20020 citations

Brueckner-Goldstone quantum Monte Carlo for correlation energies and quasiparticle energy bands of one-dimensional solids

Soohaeng Yoo Willow, Kwang S. Kim, So Hirata

A quantum Monte Carlo method that combines the second-order many-body perturbation theory and Monte Carlo (MC) integration has been developed for correlation and correlation-corrected (quasiparticle) energy bands of one-dimensional solids. The sum-of-product expressions of correlation energy and self-energy are transformed, with the aid of a Laplace transform, into high-dimensional integrals, which are subject to a highly scalable MC integration with the Metropolis algorithm for importance sampling. The method can compute correlation energies of polyacetylene and polyethylene within a few $\text{m}{E}_{\text{h}}$ and quasiparticle energy bands within a few tenths of an eV. It does not suffer from the fermion sign problem and its description can be systematically improved by raising the perturbation order.A quantum Monte Carlo method that combines the second-order many-body perturbation theory and Monte Carlo (MC) integration has been developed for correlation and correlation-corrected (quasiparticle) energy bands of one-dimensional solids. The sum-of-product expressions of correlation energy and self-energy are transformed, with the aid of a Laplace transform, into high-dimensional integrals, which are subject to a highly scalable MC integration with the Metropolis algorithm for importance sampling. The method can compute correlation energies of polyacetylene and polyethylene within a few $\text{m}{E}_{\text{h}}$ and quasiparticle energy bands within a few tenths of an eV. It does not suffer from the fermion sign problem and its description can be systematically improved by raising the perturbation order.

Physical Review BNov 18, 201420 citations

Quantum Monte-Carlo Calculations on Real Materials

Richard M. Martin, Yongkyung Kwon, Xiang Li +4 more

Springer series in solid-state sciencesJan 1, 19932 citations

Systematic comparison and cross-validation of fixed-node diffusion Monte Carlo and phaseless auxiliary-field quantum Monte Carlo in solids

Fionn D. Malone, Anouar Benali, Miguel A. Morales +3 more

Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths, and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multideterminant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis-set full configuration interaction energies estimated with CIPSI are used as a reference in this comparative study between DMC and AFQMC. By focusing on a set of canonical finite--size solid-state systems, we show that both QMC methods can be made to systematically converge towards the same energy once basis-set effects and systematic biases have been removed. AFQMC shows a much smaller dependence on the trial wave function than DMC while simultaneously exhibiting a much larger basis-set dependence. We outline some of the remaining challenges and opportunities for improving these approaches.Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths, and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multideterminant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis-set full configuration interaction energies estimated with CIPSI are used as a reference in this comparative study between DMC and AFQMC. By focusing on a set of canonical finite--size solid-state systems, we show that both QMC methods can be made to systematically converge towards the same energy once basis-set effects and systematic biases have been removed. AFQMC shows a much smaller dependence on the trial wave function than DMC while simultaneously exhibiting a much larger basis-set dependence. We outline some of the remaining challenges and opportunities for improving these approaches.

arXiv:2007.05587Physical review. B./Physical review. BOct 7, 202026 citations

\text{m}{E}_{\text{h}}

and quasiparticle energy bands within a few tenths of an eV. It does not suffer from the fermion sign problem and its description can be systematically improved by raising the perturbation order.