Convergence of many-body wavefunction expansions using a plane wave basis in the thermodynamic limit

TL;DR

This paper demonstrates that in many-body wavefunction calculations, basis set incompleteness and finite size errors can be addressed separately, enabling more efficient and accurate thermodynamic limit computations for the 2DEG system.

Contribution

It introduces a method to separately analyze and correct basis set and finite size errors in many-body wavefunction calculations, improving computational efficiency.

Findings

Errors can be separated and corrected independently in the 2DEG system.

The approach reduces computational cost by separating basis set and finite size effects.

Results are consistent with the assertion that errors can be addressed separately.

Abstract

Basis set incompleteness error and finite size error can manifest concurrently in systems for which the two effects are phenomenologically well-separated in length scale. When this is true, we need not necessarily remove the two sources of error simultaneously. Instead, the errors can be found and remedied in different parts of the basis set. This would be of great benefit to a method such as coupled cluster theory since the combined cost of $n_{occ}^6 n_{virt}^4$ could be separated into $n_{occ}^6$ and $n_{virt}^4$ costs with smaller prefactors. In this Communication, we present analysis on a data set due to Baardsen and coworkers, containing coupled cluster doubles energies for the 2DEG for $r_s=$ 0.5, 1.0 and 2.0 a.u.~at a wide range of basis set sizes and particle numbers. In obtaining complete basis set limit thermodynamic limit results, we find that within a small and removable error the above assertion is correct for this simple system. This approach allows for the combination of methods which separately address finite size effects and basis set incompleteness error.