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

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Quantum Chemistry

Background:

• Solving the Dyson equation for small-gap systems often leads to convergence issues and multiple solutions due to high non-linearity.
• Understanding electron correlation is crucial for characterizing materials like NdNiO2.

Purpose of the Study:

• To apply the homotopy continuation approach to manage iterative behavior in solving the Dyson equation.
• To locate multiple self-consistent GW solutions for the NdNiO2 solid and determine their Hartree-Fock limits.
• To investigate the nature of electron correlation and charge-density wave formation in NdNiO2.

Main Methods:

• Homotopy continuation method applied to the Dyson equation.
• Calculation of self-consistent GW solutions.
• Analysis of k-point occupations and natural difference orbitals.

Main Results:

• Successfully located multiple, qualitatively new, self-consistent GW solutions for NdNiO2.
• Identified multiple low-energy charge-transfer solutions associated with charge-density wave formation.
• Established corresponding Hartree-Fock limits for the found solutions.
• Results show qualitative agreement with experimental conductivity measurements.

Conclusions:

• The homotopy continuation approach effectively controls iterations and reveals multiple solutions for complex systems.
• The study provides new perspectives on electron correlation and charge-density waves in NdNiO2.
• Generalization of natural difference orbitals aids in understanding solutions for correlated periodic solids.