Applications of quantum Monte Carlo methods in condensed systems

Abstract

The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.

34 pages

References in corpus (87)

• Theory of ultracold Fermi gases
• Quantum Monte Carlo calculations of nuclei with A \leq 7
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• Superfluid Fermi Gases with Large Scattering Length
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• Optimization of quantum Monte Carlo wave functions by energy minimization
• Zero Temperature Phases of the Electron Gas
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Finite-size errors in continuum quantum Monte Carlo calculations
• Beyond the locality approximation in the standard diffusion Monte Carlo method
• Correlated geminal wave function for molecules: an efficient resonating valence bond approach
• Quantum Monte Carlo Studies of Superfluid Fermi Gases
• Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
• Geminal wavefunctions with Jastrow correlation: a first application to atoms
• Energy and variance optimization of many body wave functions
• Wigner crystallization and metal-insulator transition of two-dimensional holes in GaAs/AlGaAs at B=0
• Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg
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• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior
• An efficient localized basis set for quantum Monte Carlo calculations on condensed matter
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• Zero-variance principle for Monte Carlo algorithms
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• Momentum distribution and condensate fraction of a Fermi gas in the BCS-BEC crossover
• Pfaffian pairing and backflow wave functions for electronic structure quantum Monte Carlo methods
• Universal properties of a trapped two-component Fermi gas at unitarity
• Finite size errors in quantum many-body simulations of extended systems
• Proof for an upper bound in fixed-node Monte Carlo for lattice fermions
• Optimization of ground and excited state wavefunctions and van der Waals clusters
• Basis Functions for Linear-Scaling First-Principles Calculations
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• Optimized Jastrow-Slater wave functions for ground and excited states: Application to the lowest states of ethene
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• Quantum Monte Carlo calculations of structural properties of FeO under pressure
• Wave functions for quantum Monte Carlo calculations in solids: Orbitals from density functional theory with hybrid exchange-correlation functionals
• Quantum Monte Carlo for minerals at high pressure: Phase stability, equations of state, and elasticity of silica
• Hydrogen dissociation on the Mg(0001) surface from quantum Monte Carlo calculations
• Heavy-tailed random error in quantum Monte Carlo
• Renormalization factor and effective mass of the two-dimensional electron gas
• Diamond and $\beta$-tin structures of Si studied with quantum Monte Carlo calculations
• Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
• van der Waals Interactions Between Thin Metallic Wires and Layers
• Fundamental high pressure calibration from all-electron quantum Monte Carlo calculations
• Linear-scaling quantum Monte Carlo with non-orthogonal localized orbitals
• Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
• Many-body wavefunctions for normal liquid ${}^3$He
• Quantum Monte Carlo, Density Functional Theory, and Pair Potential Studies of Solid Neon
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• Transition metal oxides using quantum Monte Carlo
• Ultracold atoms at unitarity within quantum Monte Carlo
• Quantum Monte Carlo study of the two-dimensional electron gas in presence of Rashba interaction
• Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density
• Efficient Monte Carlo Calculations of the One-Body Density
• Hellman-Feynman operator sampling in Diffusion Monte Carlo calculations
• Comment on "Quantum Monte Carlo study of the dipole moment of CO" [J. Chem. Phys. 110, 11700 (1999)]
• Variational quantum Monte Carlo ground state of GaAs
• Benchmark Quantum Monte Carlo calculations of the ground-state kinetic, interaction, and total energy of the three-dimensional electron gas
• An efficient method for the Quantum Monte Carlo evaluation of the static density-response function of a many-electron system
• Fermion nodes and nodal cells of noninteracting and interacting fermions

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