arXiv subjects

P. R. C. Kent

Publications and source records attributed to P. R. C. Kent.

21 records · Page 2Linked to original sources

arXiv1999

Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions

We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in correlated sampling estimations of the energy and its variance. We investigate the numerical stability of the techniques and identify two reasons why variance minimization exhibits superior numerical stability to energy minimization. The characteristics of each method are studied using a non-interacting 64-electron model of crystalline silicon. While our main interest is in solid state systems, the issues investigated are relevant to Monte Carlo studies of atoms, molecules and solids. We identify a robust and efficient variance minimization scheme for optimizing wave functions for large systems.

cond-mat↗

arXiv1998

Finite size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.

cond-mat↗

arXiv1998

Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon

Quantum Monte Carlo (QMC) techniques are used to calculate the one-body density matrix and excitation energies for the valence electrons of bulk silicon. The one-body density matrix and energies are obtained from a Slater-Jastrow wave function with a determinant of local density approximation (LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is strongly diagonally dominant. The natural orbitals obtained by diagonalizing the QMC density matrix resemble the LDA orbitals very closely. Replacing the determinant of LDA orbitals in the wave function by a determinant of natural orbitals makes no significant difference to the quality of the wave function's nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended Koopmans' Theorem for correlated wave functions is used to calculate excitation energies for silicon, which are in reasonable agreement with the available experimental data. A diagonal approximation to the theorem, evaluated in the basis of LDA orbitals, works quite well for both the quasihole and quasielectron states. We have found that this approximation has an advantageous scaling with system size, allowing more efficient studies of larger systems.

cond-mat↗