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

TL;DR

This paper introduces a real-time path integral method for accurately calculating strongly correlated electronic systems, demonstrated on a 1D Hooke's atom, and compares it with Diffusion Monte Carlo, highlighting new computational tools and hybrid approaches.

Contribution

The paper presents incoherent RTPI as a novel method for ground state calculation, offering advantages over DMC, and explores combining these methods for improved accuracy in strongly correlated systems.

Findings

Incoherent RTPI effectively finds ground states in strongly correlated systems.

Monte Carlo grid is efficient for path integral calculations.

Combining iRTPI and DMC enhances simulation capabilities.

Abstract

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.