Local Hamiltonians for quantitative Green's function embedding methods

TL;DR

This paper introduces a new method for directly parametrizing impurity Hamiltonians in Green's function embedding, bypassing traditional low-energy model construction, leading to accurate energies and self-energies for large molecules and solids.

Contribution

A novel impurity Hamiltonian parametrization technique that directly recovers the system's self-energy, improving embedding calculations without uncontrolled low-energy model assumptions.

Findings

Accurate total energies and self-energies achieved

Impurity Hamiltonian effectively captures non-local interactions

Method improves embedding calculations for large systems

Abstract

Embedding calculations that find approximate solutions to the Schr\"{o}dinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective interactions approximating the low energy physics of the initial realistic system, (ii) mapping the model system onto an impurity Hamiltonian, and (iii) solving the impurity problem. We have developed a novel procedure for parametrizing the impurity Hamiltonian that avoids the mathematically uncontrolled step of constructing the low energy model system. Instead, the impurity Hamiltonian is immediately parametrized to recover the self-energy of the realistic system in the limit of high frequencies or short time. The effective interactions parametrizing the fictitious impurity Hamiltonian are local to the embedded regions, and include all the non-local interactions present in the original realistic Hamiltonian in an implicit way. We show that this impurity Hamiltonian can lead to excellent total energies and self-energies that approximate the quantities of the initial realistic system very well. Moreover, we show that as long as the effective impurity Hamiltonian parametrization is designed to recover the self-energy of the initial realistic system for high frequencies, we can expect a good total energy and self-energy. Finally, we propose two practical ways of evaluating effective integrals for parametrizing impurity models.