Predictive Capability for Strongly Correlated Systems

Diffusion Monte Carlo methods can give highly accurate results for correlated systems, provided that well optimized trial wave functions with accurate nodal surfaces are employed. The Cornell team developed powerful methods for optimizing all the parameters within a multi-determinant Slater-Jastrow form of the wave function. These include the Jastrow parameters within a flexible electron-electron-nucleus form of the Jastrow function, the parameters multiplying the configuration state functions, the orbital parameters and the basis exponents. The method optimizes a linear combination of the energy and the variance of the local energy. The optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. It is highly robust, has become the method of choice for correlated wave function optimization and has been adopted by other QMC groups. This optimization method was used on the first-row atoms and homonuclear diatomic molecules, demonstrating that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems. In addition the complete ground-state potential energy curve of the C{sub 2} molecule up to the dissociation limit was obtained, and, size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations were studied. The method was used with a eight-electrons-in-eight-orbitals complete active space CAS(8,8) wave function to study the relative energies of the monocyclic and bicyclic forms of m-benzyne. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.92 kcal/ mole, which is in excellent agreement with the best coupled cluster results (CCSD(T)) and in disagreement with the CCSD results. QMC methods have for the most part been used only for ground states of a given symmetry. We developed a method for calculating low-lying excited states as well and tested it on the ground and lowest three adiabatic excited states of methylene with progressively larger JastrowSlater multideterminant complete active space CAS wave functions. The highest of these states has the same symmetry, {sup 1}A{sub 1}, as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment. In contrast, single-determinant wave functions do not yield accurate DMC energies, indicating that it is important to include in the wave function Slater determinants that describe static strong correlation

Approximating strongly correlated spin and fermion wavefunctions with correlator product states

We explore correlator product states for the approximation of correlated wavefunctions in arbitrary dimensions. We show that they encompass many interesting states including Laughlin's quantum Hall wavefunction, Huse and Elser's frustrated spin states, and Kitaev's toric code. We further establish their relation to common families of variational wavefunctions, such as matrix and tensor product states and resonating valence bond states. Calculations on the Heisenberg and spinless Hubbard models show that correlator product states capture both two-dimensional correlations (independent of system width) as well as non-trivial fermionic correlations (without sign problems). In one-dimensional simulations, correlator product states appear competitive with matrix product states with a comparable number of variational parameters, suggesting they may eventually provide a route to practically generalise the density matrix renormalisation group to higher dimensions.Comment: Table 1 expanded, Table 2 updated, optimization method discussed, discussions expanded in some sections, earlier work on similar wavefunctions included in text and references, see also (arXiv:0905.3898). 5 pages, 1 figure, 2 tables, submitted to Phys. Rev.

Repulsive interaction of the helium atom with a metal surface

The repulsive part of the helium scattering potential at a surface is approximately proportional to the surface electron density. The proportionality coefficient is shown to be a well-defined quantity, which can be related to the electron-helium scattering length. The spread in the values of the proportionality constant suggested in the literature is shown to be due to different definitions of the coefficient or due to inadequate calculational methods. The value calculated using the local density approximation with a self-interaction correction is in very good agreement with the electron-scattering-length measurements.Peer reviewe

Predictive Capability for Strongly Correlated Systems

Diffusion Monte Carlo methods can give highly accurate results for correlated systems, provided that well optimized trial wave functions with accurate nodal surfaces are employed. The Cornell team developed powerful methods for optimizing all the parameters within a multi-determinant Slater-Jastrow form of the wave function. These include the Jastrow parameters within a flexible electron-electron-nucleus form of the Jastrow function, the parameters multiplying the configuration state functions, the orbital parameters and the basis exponents. The method optimizes a linear combination of the energy and the variance of the local energy. The optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. It is highly robust, has become the method of choice for correlated wave function optimization and has been adopted by other QMC groups. This optimization method was used on the first-row atoms and homonuclear diatomic molecules, demonstrating that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems. In addition the complete ground-state potential energy curve of the C{sub 2} molecule up to the dissociation limit was obtained, and, size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations were studied. The method was used with a eight-electrons-in-eight-orbitals complete active space CAS(8,8) wave function to study the relative energies of the monocyclic and bicyclic forms of m-benzyne. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.92 kcal/ mole, which is in excellent agreement with the best coupled cluster results (CCSD(T)) and in disagreement with the CCSD results. QMC methods have for the most part been used only for ground states of a given symmetry. We developed a method for calculating low-lying excited states as well and tested it on the ground and lowest three adiabatic excited states of methylene with progressively larger JastrowSlater multideterminant complete active space CAS wave functions. The highest of these states has the same symmetry, {sup 1}A{sub 1}, as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment. In contrast, single-determinant wave functions do not yield accurate DMC energies, indicating that it is important to include in the wave function Slater determinants that describe static strong correlation

Surface-Wave-Induced Interference Effects in Angle-Resolved Photoemission

New features are observed in normal-emission photoelectron spectra from Ni(100) in a narrow range of photon energies around 25 eV. These features are inconsistent with either direct transitions from the bulk or emission from occupied surface states or resonances. We suggest that they are a consequence of interference between the ordinary direct transition emitting an electron in the normal direction and the excitation from the same initial state into a final state that would normally be emitted from the surface at Γ― in the second surface Brillouin zone, but at this energy is trapped in a surface wave

ITR: Modelling and simulations of quantum phenomena in semiconductor structures of reduced dimensions

Issued as final reportWe are conducting first-principles simulations of the atomic configurations, electronic structure, dynamic properties, and transport in semiconductor nanowires and nanostructures using computational methods based on density functional theory and quantum Monte Carlo approaches. Specific projects include calculations of the band gap and optical properties of various semiconductor nanowires, transport in the presence of aluminum contact electrodes, vibrational and thermal properties of nanostructures, and electron correlation in two-dimensional quantum dots. We have also worked on the formulation of superconductivity-induced contributions to the cohesive energy and elongation-forces in metallic nanowires.National Science Foundation (U.S.