Excitations and spectra from equilibrium real-time Green's functions

Abstract

The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the storage requirements of the discretized Green's function and the computational cost of solving the Dyson equation. In this manuscript, we apply a real-time discretization based on a piece-wise high-order orthogonal-polynomial expansion to address these issues. We present a superconvergent algorithm for solving the real-time equilibrium Dyson equation using the Legendre spectral method and the recursive algorithm for Legendre convolution. We show that the compact high order discretization in combination with our Dyson solver enables long-time simulations using far fewer discretization points than needed in conventional multistep methods. As a proof of concept, we compute the molecular spectral functions of H${}_2$, LiH, He${}_2$ and C${}_6$H${}_4$O${}_2$ using self-consistent second-order perturbation theory and compare the results with standard quantum chemistry methods as well as the auxiliary second-order Green's function perturbation theory method.

References in corpus (54)

• Recent developments in the PySCF program package
• Nonequilibrium dynamical mean-field theory and its applications
• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Quantum Algorithms for Fermionic Simulations
• Solving strongly correlated electron models on a quantum computer
• Hybrid quantum-classical approach to correlated materials
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Spectral functions in one-dimensional quantum systems at T>0
• The Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Levels of self-consistency in the GW approximation
• Self-consistent GW: All-electron implementation with localized basis functions
• 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
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters
• Nevanlinna Analytical Continuation
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• NESSi: The Non-Equilibrium Systems Simulation package
• Time-propagation of the Kadanoff-Baym equations for inhomogeneous systems
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Breakdown of traditional many-body theories for correlated electrons
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Second-order Green's function perturbation theory for periodic systems
• Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory
• First-principles nonequilibrium Green's function approach to transient photoabsorption: Application to atoms
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Discrete Lehmann representation of imaginary time Green's functions
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Exact Ionization Potentials from Wavefunction Asymptotics: The Extended Koopmans' Theorem, Revisited
• Low rank compression in the numerical solution of the nonequilibrium Dyson equation
• 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
• Efficient temperature-dependent Green's functions methods for realistic systems: compact grids for orthogonal polynomial transforms
• Chebyshev polynomial representation of imaginary time response functions
• Some Exact Properties of the Nonequilibrium Response Function for Transient Photoabsorption
• irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green's function
• Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions
• Fractional charge and spin errors in self-consistent Green's function theory
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory
• Legendre-spectral Dyson equation solver with super-exponential convergence
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• Effect of propagator renormalization on the band gap of insulating solids
• Adaptive Numerical Solution of Kadanoff-Baym Equations
• Spectral properties from Matsubara Green's function approach - application to molecules
• A wave function perspective and efficient truncation of renormalised second-order perturbation theory
• Memory truncated Kadanoff-Baym equations
• Efficient excitations and spectra within a perturbative renormalization approach
• Exact Diagonalization library for quantum electron models
• Phase transitions in partial summation methods: Results from the 3D Hubbard model
• Beyond the Hubbard bands in strongly correlated lattice bosons

Cited by in corpus (5)

• Time-linear quantum transport simulations with correlated nonequilibrium Green's functions
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Minimal pole representation for spectral functions
• Equivariant neural network for Green's functions of molecules and materials
• Chirped amplitude mode in photo-excited superconductors