Systematic reduction of sign errors in many-body problems: generalization of self-healing diffusion Monte Carlo to excited states

Abstract

A recently developed self-healing diffusion Monte Carlo algorithm [PRB 79, 195117] is extended to the calculation of excited states. The formalism is based on an excited-state fixed-node approximation and the mixed estimator of the excited-state probability density. The fixed-node ground state wave-functions of inequivalent nodal pockets are found simultaneously using a recursive approach. The decay of the wave-function into lower energy states is prevented using two methods: i) The projection of the improved trial-wave function into previously calculated eigenstates is removed. ii) The reference energy for each nodal pocket is adjusted in order to create a kink in the global fixed-node wave-function which, when locally smoothed out, increases the volume of the higher energy pockets at the expense of the lower energy ones until the energies of every pocket become equal. This reference energy method is designed to find nodal structures that are local minima for arbitrary fluctuations of the nodes within a given nodal topology. We demonstrate in a model system that the algorithm converges to many-body eigenstates in bosonic-like and fermionic cases.

New version with two new figures. Several formulas of intermediate steps in the analytical derivations have been added. The review reports and replies with a summary of changes are included in the source pdf files with nicer figures are also included in the source

References in corpus (4)

• Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: potential energy curves of low lying C2 singlet states
• Self-healing diffusion quantum Monte Carlo algorithms: methods for direct reduction of the fermion sign error in electronic structure calculations
• A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
• Density-density functionals and effective potentials in many-body electronic structure calculations

Cited by in corpus (3)

• Systematic reduction of sign errors in many-body calculations of atoms and molecules
• Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons
• Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body bases