Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices

Abstract

Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular solutions was not performed before. In this work, we use two-particle density matrices to investigate local spin and charge correlators that quantify the charge-resonance and covalent characters of these solutions. When applied within unrestricted orbital set, spin correlators elucidate the broken symmetry of the solutions, containing necessary information for building effective magnetic Hamiltonians. Based on GW and GF2 calculations of simple molecules and transition metal complexes, we construct Heisenberg Hamiltonians, four-spin-four-center corrections, as well as biquadratic spin-spin interactions. These Hamiltonian parametrizations are compared to prior wave-function calculations.

References in corpus (19)

• The GW method
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Fully self-consistent GW calculations for atoms and molecules
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Second-order Green's function perturbation theory for periodic systems
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Ground State Properties of Simple Elements from GW Calculations
• The self-consistent Dyson equation and self-energy functionals: failure or new opportunities?
• Ab-Initio self-energy embedding for the photoemission spectra of NiO and MnO
• Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function
• Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions
• Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2
• Effect of propagator renormalization on the band gap of insulating solids
• Exact Diagonalization library for quantum electron models
• Is solid copper oxalate a spin chain or a mixture of entangled spin pairs?
• Broken-symmetry-adapted Green function theory of condensed matter systems:towards a vector spin-density-functional theory

Cited by in corpus (5)

• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations
• Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Phase transitions in partial summation methods: Results from the 3D Hubbard model