The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform

Paul R. C. Kent - One of the best experts on this subject based on the ideXlab platform.

  • Delayed Slater Determinant update algorithms for high efficiency quantum Monte Carlo
    The Journal of chemical physics, 2017
    Co-Authors: Tyler Mcdaniel, Ed F D'azevedo, Kwai Wong, Paul R. C. Kent
    Abstract:

    Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater Determinants in the trial wavefunction. Each Monte Carlo step requires finding the Determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core CPUs and GPUs.

  • delayed Slater Determinant update algorithms for high efficiency quantum monte carlo
    Journal of Chemical Physics, 2017
    Co-Authors: Tyler Mcdaniel, Kwai Wong, Ed F Dazevedo, Paul R. C. Kent
    Abstract:

    Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater Determinants in the trial wavefunction. Each Monte Carlo step requires finding the Determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carl...

  • a fast and efficient algorithm for Slater Determinant updates in quantum monte carlo simulations
    Journal of Chemical Physics, 2009
    Co-Authors: Phani K V V Nukala, Paul R. C. Kent
    Abstract:

    We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater Determinants. In particular, the computational complexity of the algorithm is O(kN) during the kth step compared to traditional algorithms that require O(N2) computations, where N is the system size. For single Determinant trial wave functions the new algorithm is faster than the traditional O(N2) Sherman–Morrison algorithm for up to O(N) updates. For multiDeterminant configuration-interaction-type trial wave functions of M+1 Determinants, the new algorithm is significantly more efficient, saving both O(MN2) work and O(MN2) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.

F. G. Eich - One of the best experts on this subject based on the ideXlab platform.

  • Overhauser's spin-density wave in exact-exchange spin-density functional theory
    Physical Review B, 2009
    Co-Authors: Stefan Kurth, F. G. Eich
    Abstract:

    The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in HartreeFock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater Determinant with energy lower than the corresponding paramagnetic state, this Slater Determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater Determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.

  • Overhauser's spin-density wave in exact-exchange spin-density functional theory
    Physical Review B, 2009
    Co-Authors: Stefan Kurth, F. G. Eich
    Abstract:

    The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in HartreeFock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater Determinant with energy lower than the corresponding paramagnetic state, this Slater Determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater Determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.

D Pfirsch - One of the best experts on this subject based on the ideXlab platform.

Thomas D Kuhne - One of the best experts on this subject based on the ideXlab platform.

Stefan Kurth - One of the best experts on this subject based on the ideXlab platform.

  • Overhauser's spin-density wave in exact-exchange spin-density functional theory
    Physical Review B, 2009
    Co-Authors: Stefan Kurth, F. G. Eich
    Abstract:

    The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in HartreeFock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater Determinant with energy lower than the corresponding paramagnetic state, this Slater Determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater Determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.

  • Overhauser's spin-density wave in exact-exchange spin-density functional theory
    Physical Review B, 2009
    Co-Authors: Stefan Kurth, F. G. Eich
    Abstract:

    The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in HartreeFock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater Determinant with energy lower than the corresponding paramagnetic state, this Slater Determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater Determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.