Overcomplete compact representation of two-particle Green's functions

Abstract

Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Green's functions in terms of an overcomplete representation based on the recently proposed "intermediate representation" basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Green's function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.

arXiv comment17 pages, 12 figures (minor modifications)

References in corpus (29)

• Scikit-learn: Machine Learning in Python
• A continuous-time solver for quantum impurity models
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Local Electronic Correlation at the Two-Particle Level
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Mott physics and spin fluctuations: a unified framework
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• From infinite to two dimensions through the functional renormalization group
• Efficient perturbation theory for quantum lattice models
• Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
• Ab initio dynamical vertex approximation
• The magnetic excitation spectra in BaFe${}_2$As${}_2$: a two-particle approach within DFT+DMFT
• One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT
• Efficient treatment of two-particle vertices in dynamical mean-field theory
• Parquet decomposition calculations of the electronic self-energy
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• FLEX+DMFT approach to the $d$-wave superconducting phase diagram of the two-dimensional Hubbard model
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Superperturbation solver for quantum impurity models
• Critical Exponents of Strongly Correlated Fermion Systems from Diagrammatic Multi-Scale Methods
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Hidden physics in the dual-fermion approach - a special case of a non-local expansion scheme
• LDA+DMFT approach to ordering phenomena and the structural stability of correlated materials
• Spectral properties of four-time fermionic Green's functions

Cited by in corpus (36)

• Sparse sampling approach to efficient ab initio calculations at finite temperature
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Discrete Lehmann representation of imaginary time Green's functions
• sparse-ir: optimal compression and sparse sampling of many-body propagators
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Multipoint correlation functions: spectral representation and numerical evaluation
• Sparse Modeling in Quantum Many-Body Problems
• irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green's function
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• Sparse sampling and tensor network representation of two-particle Green's functions
• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
• Solving the Bethe-Salpeter equation with exponential convergence
• Metal-insulator transition in the 2D Hubbard model: dual fermion approach with the Lanczos exact diagonalization
• Robust analytic continuation combining the advantages of the sparse modeling approach and Padé approximation
• Two-particle calculations with quantics tensor trains: Solving the parquet equations
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Smooth self-energy in the exact-diagonalization-based dynamical mean-field theory: Intermediate-representation filtering approach
• Compactness of quantics tensor train representations of local imaginary-time propagators
• Stochastic pole expansion method
• Minimal pole representation for spectral functions
• Statistical error estimates in dynamical mean-field theory and extensions thereof
• Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory
• Effects of orbital selective dynamical correlation on the spin susceptibility and superconducting symmetries in Sr${}_2$RuO${}_4$
• Second-order dual fermion for multi-orbital systems
• Compressing the two-particle Green's function using wavelets: Theory and application to the Hubbard atom
• Discrete Lehmann representation of three-point functions
• Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• All electron GW with linearized augmented plane waves for metals and semiconductors
• Phase transition in binary compressed sensing based on $L_1$-norm minimization
• Navigating the trends in the proximity to magnetic quantum critical point and superconductivity for Ce-based heavy-fermion compounds
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting
• Imaginary Time Formalism for Causal Nonlinear Response Functions