Local Hamiltonians for quantitative Green's function embedding methods

Abstract

Embedding calculations that find approximate solutions to the Schrödinger 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.

11 pages, 10 figures

References in corpus (7)

• Continuous-time Monte Carlo methods for quantum impurity models
• Screened Coulomb interaction in the maximally localized Wannier basis
• Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Embedded density functional theory for covalently bonded and strongly interacting subsystems
• Dynamical Mean-Field Theory for Quantum Chemistry

Cited by in corpus (33)

• Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
• Nevanlinna Analytical Continuation
• Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Finite temperature quantum embedding theories for correlated systems
• Self-energy embedding theory (SEET) for periodic systems
• Charge ordering and correlation effects in the extended Hubbard model
• Generalized self-energy embedding theory
• Connections and performances of Green's function methods for charged and neutral excitations
• Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy
• 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
• Unphysical Discontinuities in GW Methods
• Chebyshev polynomial representation of imaginary time response functions
• Efficient temperature-dependent Green's function methods for realistic systems: using cubic spline interpolation to approximate Matsubara Green's functions
• Charge order and antiferromagnetism in the extended Hubbard model
• Fractional charge and spin errors in self-consistent Green's function theory
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Energy-weighted density matrix embedding of open correlated chemical fragments
• Reference Energies for Valence Ionizations and Satellite Transitions
• Testing self-energy embedding theory in combination with GW
• Iterative subspace algorithms for finite-temperature solution of Dyson equation
• A similarity renormalization group approach to Green's function methods
• Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
• Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2
• Connections between many-body perturbation and coupled-cluster theories
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions
• Exploring Coupled Cluster Green's function as a method for treating system and environment in Green's function embedding methods
• Constructing `full-frequency' spectra via moment constraints for coupled cluster Green's functions
• Complex Absorbing Potential Green's Function Methods for Resonances
• The Future of the Correlated Electron Problem
• Single- and two-particle finite size effects in interacting lattice systems
• Sparse-Hamiltonian approach to the time evolution of molecules on quantum computers