Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2

TL;DR

This paper introduces a homotopy continuation method to solve the Dyson equation self-consistently, addressing convergence issues and discovering multiple solutions in NdNiO2 that reveal new insights into electron correlation and charge-density waves.

Contribution

The study applies homotopy continuation to the Dyson equation, enabling the identification of multiple solutions and providing a new approach to understanding correlated electron systems.

Findings

Multiple self-consistent GW solutions for NdNiO2 were found.

Some solutions reveal charge-density waves consistent with experiments.

The method helps understand electron correlation in small-gap systems.

Abstract

Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the homotopy continuation approach to control the behavior of iterations. We used the homotopy continuation to locate multiple fully self-consistent GW solutions for NdNiO2 solid and to establish the corresponding Hartree-Fock limits. Some of the solutions found are qualitatively new and help to understand the nature of electron correlation in this material. We show that there are multiple low-energy charge-transfer solutions leading to a formation of charge-density waves. Our results qualitatively agree with the experimental conductivity measurements. To rationalize the structure of solutions, we compare the k-point occupations and generalize the concept of natural difference orbitals for correlated periodic solids.