Finite-size errors in continuum quantum Monte Carlo calculations

We analyze the problem of eliminating finite-size errors from quantum Monte Carlo (QMC) energy data. We demonstrate that both (i) adding a recently proposed [S. Chiesa et al., Phys. Rev. Lett. 97, 076404 (2006)] finite-size correction to the Ewald energy and (ii) using the model periodic Coulomb (MPC) interaction [L. M. Fraser et al., Phys. Rev. B 53, 1814 (1996); P. R. C. Kent et al., Phys. Rev. B 59, 1917 (1999); A. J. Williamson et al., Phys. Rev. B 55, 4851 (1997)] are good solutions to the problem of removing finite-size effects from the interaction energy in cubic systems, provided the exchange-correlation (XC) hole has converged with respect to system size. However, we find that the MPC interaction distorts the XC hole in finite systems, implying that the Ewald interaction should be used to generate the configuration distribution. The finite-size correction of Chiesa et al. is shown to be incomplete in systems of low symmetry. Beyond-leading-order corrections to the kinetic energy are found to be necessary at intermediate and high densities, and we investigate the effect of adding such corrections to QMC data for the homogeneous electron gas. We analyze finite-size errors in two-dimensional systems and show that the leading-order behavior differs from that which has hitherto been supposed. We compare the efficiency of different twist-averaging methods for reducing single-particle finite-size errors and we examine the performance of various finite-size extrapolation formulas. Finally, we investigate the system-size scaling of biases in diffusion QMC

Uniaxial Phase Transition in Si : Ab initio Calculations

Based on a previously proposed thermodynamic analysis, we study the relative stabilities of five Si phases under uniaxial compression using ab initio methods. The five phases are diamond, beta-tin, sh, sc, and hcp structures. The possible phase-transition patterns were investigated by considering the phase transitions between any two chosen phases of the five phases. By analyzing the different conributions to the relative pahse stability, we identified the most important factors in reducing the phase-transition pressures at uniaxial compression. We also show that it is possible to have phase transitions occur only when the phases are under uniaxial compression, in spite of no phase transition when under hydrostatic commpression. Taking all five phases into consideration, the phase diagram at uniaxial compression was constructed for pressures under 20 GPa. The stable phases were found to be diamond, beta-tin and sh structures, i.e. the same as those when under hydrostatic condition. According to the phase diagram, direct phase transition from the diamond to the sh phase is possible if the applied uniaxial pressures, on increasing, satisfy the condition of Px>Pz. Simiilarly, the sh-to-beta-tin transition on increeasing pressures is also possible if the applied uniaxial pressures are varied from the condition of Px>Pz, on which the phase of sh is stable, to that of Px<Pz, on which the beta-tin is stable

Excitons in T-shaped quantum wires

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/Al$_{x}$Ga$_{1-x}$As and In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction $x$. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/Al$_{x}$Ga$_{1-x}$As wires we obtain an upper limit for the binding energy of around 25 meV in a 10 {\AA} wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that In$_{y}$Ga$_{1-y}$As/Al$_{x}$Ga$_{1-x}$As might be a good candidate.Comment: 20 pages, 10 figures, uses RevTeX and psfig, submitted to Physical Review

Quantum Monte Carlo calculations of the surface energy of an electron gas

Published versio

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.Comment: 14 pages, including 7 figures. To appear in Phys. Rev. B. For related publications see http://www.tcm.phy.cam.ac.uk/Publications/many_body.htm

Surface energy and stability of stress-driven discommensurate surface structures

A method is presented to obtain {\it ab initio} upper and lower bounds to surface energies of stress-driven discommensurate surface structures, possibly non-periodic or exhibiting very large unit cells. The instability of the stressed, commensurate parent of the discommensurate structure sets an upper bound to its surface energy; a lower bound is defined by the surface energy of an ideally commensurate but laterally strained hypothetical surface system. The surface energies of the phases of the Si(111):Ga and Ge(111):Ga systems and the energies of the discommensurations are determined within $\pm 0.2$ eV.Comment: 4 pages RevTeX. 2 Figures not included. Ask for a hard copy (through regular mail) to [email protected]

A fourfold coordinated point defect in silicon

Due to their technological importance, point defects in silicon are among the best studied physical systems. The experimental examination of point defects buried in bulk is difficult and evidence for the various defects usually indirect. Simulations of defects in silicon have been performed at various levels of sophistication ranging from fast force fields to accurate density functional calculations. The generally accepted viewpoint from all these studies is that vacancies and self interstitials are the basic point defects in silicon. We challenge this point of view by presenting density functional calculations that show that there is a new fourfold coordinated point defect in silicon that is lower in energy

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.Comment: 13 pages, 4 figures. To appear in Phys. Rev.

A Geometric Formulation of Quantum Stress Fields

We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.Comment: 22 pages, 2 figures. Submitted to Physical Review B. This paper supersedes cond-mat/000627

Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon

The band structure of silicon is calculated at the Gamma, X, and L wave vectors using diffusion quantum Monte Carlo methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low lying excitations in solids.Comment: 5 pages, 1 figur