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arXiv · 2507.00290

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

Pavel Pokhilko·Dominika Zgid
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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.

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Pavel Pokhilko, Dominika Zgid. 2025-06-30. Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2. https://arxiv.org/abs/2507.00290

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