Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space

Abstract

We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces. The new method is a population dynamics of a set of walkers, and is designed to simulate the underlying imaginary-time Schrödinger equation of the interacting Hamiltonian. The walkers (which carry a positive or negative sign) inhabit Slater determinant space, and evolve according to a simple set of rules which include spawning, death and annihilation processes. We show that this method is capable of converging onto the full configuration-interaction (FCI) energy and wave function of the problem, without any a priori information regarding the nodal structure of the wave function being provided. Walker annihilation is shown to play a key role. The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. At this point, the correlation energy can be measured using two independent methods--a projection formula and a energy shift; agreement between these provides a strong measure of confidence in the accuracy of the computed correlation energies. We have verified the method by performing calculations on systems for which FCI calculations already exist. In addition, we report on a number of new systems, including CO, O(2), CH(4), and NaH--with FCI spaces ranging from 10(9) to 10(14), whose FCI energies we compute using modest computational resources.

Using CIPSI Nodes in Diffusion Monte Carlo

“…We note that the recent FCI-QMC method of Alavi et al [9,10] uses essentially the same idea, except that in CIPSI the selection is done deterministically instead of stochastically.…”

“…[8] CIPSI being our working algorithm for generating CI expansions, a brief description is given here. It is noted that the recent FCI-QMC method of Alavi et al [9,10] is essentially a SCI approach, except that selection of determinants in FCI-QMC is done stochastically instead of deterministically.…”

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models

“…FCI Quantum Monte Carlo and its 'initiator' adaptation (i-FCIQMC) are novel methods developed in a series of recent papers [11][12][13][14][15][16] in which the FCI equations are simulated by representing the determinant coefficients as a set of walkers evolving over discretized imaginary time. This allows much larger Hilbert spaces to be studied, with the largest space accurately sampled to date being 10 108 , in a previous study of the 54-electron gas 16 .…”

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

“…The most widely employed scheme to reduce the problem to polynomial complexity is the Fixed-Node (FN) approximation [16,17]: FN restricts the stochastic sampling of the configurational space to regions where the sign of a reasonable approximation for the ground state wave function, the trial wave function, remains constant. Such approximation provides very accurate estimations of ground state properties [16][17][18][19]. Nevertheless, FN may give inaccurate results for imaginary time correlation functions even when the nodal structure of the ground state wavefunction is exactly known: as an example, in Fig.…”

“…[18,[20][21][22]24]. In the present work we consider one of such QMC methods, the phaseless Auxiliary Fields Quantum Monte Carlo (AFQMC) [20,22,25], which is considered less sensitive than FN to the quality of the trial function [29].…”