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Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke’s atom

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)45-53
Number of pages9
JournalComputer Physics Communications
Early online date4 Oct 2016
Publication statusPublished - Jan 2017
Publication typeA1 Journal article-refereed


We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke’s atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.


  • Path integral, Quantum dynamics, First-principles, Monte Carlo, Strong correlation, Hooke’s atom

Publication forum classification

Field of science, Statistics Finland