Constrained Random Phase Approximation: the spectral method

TL;DR

This paper introduces a spectral cRPA method that improves the accuracy and stability of Hubbard U calculations, aligning better with experimental data and addressing limitations of conventional cRPA approaches.

Contribution

The paper presents a novel spectral cRPA method that enhances numerical stability and accuracy in calculating electron interactions, especially for complex materials.

Findings

s-cRPA yields larger U values than conventional methods.

s-cRPA aligns better with experimental insulating states in CaFeO3.

The method improves numerical stability by conserving electron number.

Abstract

We present a constrained Random Phase Approximation (cRPA) method, termed spectral cRPA (s-cRPA), and compare it to established cRPA approaches for Scandium and Copper by varying the 3d shell filling. The s-cRPA method generally produces larger Hubbard U interaction values compared to conventional approaches. When applied to the realistic system CaFeO$_3$ , s-cRPA yields interaction parameters that align more closely with those required within DFT+U to reproduce the experimentally observed insulating state, addressing the metallic behaviour predicted by standard density functionals. We examine the issue of negative interaction values encountered in the projector cRPA method for filled d-shells. We show that s-cRPA provides improved numerical stability by preserving electron number conservation, a constraint that is violated in the projector cRPA method. The s-cRPA approach addresses some limitations of standard cRPA methods, particularly the tendency to underestimate U values, suggesting its potential utility for the community. Additionally, we have enhanced our implementation to include computation of multi-centre interactions for analysing spatial decay and developed an efficient low-scaling variant employing a compressed Matsubara grid to obtain full frequency-dependent interactions.