Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

TL;DR

This paper demonstrates that by modifying FCIQMC to sample only seniority zero space, DOCI and pCCD energies align for 2D Hubbard models, offering a computationally efficient approach to strong correlation problems.

Contribution

The authors adapt FCIQMC to sample only seniority zero space, enabling efficient comparison of DOCI and pCCD energies in complex Hubbard models.

Findings

DOCI and pCCD energies agree in 2D Hubbard models.

Seniority zero space reduces the sign problem significantly.

Modified FCIQMC effectively samples seniority zero configurations.

Abstract

Over the past few years pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this, and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.