Constrained Random Phase Approximation: the spectral method

• URL: http://arxiv.org/abs/2508.15368v3
• Date: Tue, 23 Sep 2025 15:15:51 GMT
• Title: Constrained Random Phase Approximation: the spectral method
• Abstract summary: We present a constrained Random Phase Approximation (cRPA) method, termed spectral cRPA (s-cRPA)<n>We compare it to established cRPA approaches for Scandium and Copper by varying the 3d shell filling.
• Score: 35.29742953849465
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 projec- tor 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. Addi- tionally, 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.

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