Self-healing Diffusion Quantum Monte Carlo Algorithms: Direct Reduction of the Fermion Sign Error in Electronic Structure Calculations
Accurately solving the many electron Schrödinger equation for real materials is a holy grail of condensed matter physics and materials science. Currently Diffusion Monte Carlo (DMC) represents state of the art, both in terms of the accuracy that can be achieved and the number of electrons that can be treated (i.e. system complexity). To date a major limitation on the accuracy of DMC solution has been the so called fixed node approximation for the trial wave function that is used to guide the quantum Monte Carlo calculation – an approximation that allows one to circumvent the notorious “sign” problem associated with quantum Monte Carlo methods for Fermion systems.
We have developed a self-healing Diffusion Monte Carlo (SH-DMC) method for calculating the ground-state properties of many electron systems. The method allows for systematic improvement of the nodal structure of the trial wave-function. The basic algorithm was recently published in Physical Review B. Ongoing tests on small systems (e.g. C20 and LiSr) support the possibility of treating correlated electron systems with unprecedented size and complexity.
Research performed at the Materials Science and Technology Division and the Center for Nanophase Materials Sciences at Oak Ridge National Laboratory was sponsored by the Division of Materials Sciences and the Division of Scientific User Facilities U.S. Department of Energy. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory.
F. A. Reboredo, R. Q. Hood, and P. R. C. Kent, Phys. Rev. B 79, 195117 (2009)