Brueckner-Goldstone quantum Monte Carlo for correlation energies and quasiparticle energy bands of one-dimensional solids

A quantum Monte Carlo method that combines the second-order many-body perturbation theory and Monte Carlo (MC) integration has been developed for correlation and correlation-corrected (quasiparticle) energy bands of one-dimensional solids. The sum-of-product expressions of correlation energy and self-energy are transformed, with the aid of a Laplace transform, into high-dimensional integrals, which are subject to a highly scalable MC integration with the Metropolis algorithm for importance sampling. The method can compute correlation energies of polyacetylene and polyethylene within a few mEh and quasiparticle energy bands within a few tenths of an eV. It does not suffer from the fermion sign problem and its description can be systematically improved by raising the perturbation order.