Model-mapped RPA for determining the effective Coulomb interaction

TL;DR

This paper introduces a novel RPA-based method to derive effective Coulomb interactions in model Hamiltonians, explicitly considering long-range polarization effects, demonstrated on a high-temperature superconductor model.

Contribution

The new method improves upon previous RPA approaches by incorporating long-range polarization effects in the calculation of effective interactions.

Findings

Successfully applied to the single-band Hubbard model of HgBa₂CuO₄

Addresses limitations of previous RPA methods

Provides more accurate effective interaction parameters

Abstract

We present a new method to obtain interaction part of a model Hamiltonian from the result of the first-principles calculation. The effective interaction contained in the model is determined based on the random phase approximation (RPA). In contrast to previous methods such as projected RPA or constrained RPA, the new method takes into account the long-range part of the polarization effect when determining the interaction in the model. After we discuss problems in previous RPA methods, we will give the formulation of the new method, and show how it works for the single-band Hubbard model of HgBa$_2$CuO$_4$.