Computation Kernel for Feynman Diagrams
arXiv:2503.08444 · doi:10.1103/wdy1-l2t2
Abstract
We present a general representation for solving problems in many-body perturbation theory. By projecting the single-particle Green's function to an auxiliary space we show how one can convert an arbitrary Feynman graph to a universal kernel representation. Once constructed, the computation kernel contains no problem specific information yet contains all explicit temperature and frequency dependence of the diagram. This computation kernel is problem agnostic, and valid for any physical problem that would normally leverage the Matsubara formalism of many-body perturbation theory. The result of any diagram can be written as a linear combination of these computation kernel elements with coefficients given by a sum over products of known tensor elements that are themselves problem specific and represent spatial degrees of freedom. We probe the efficacy of this approach by generating the computation kernel for a low order self-energy diagram which we then use to construct solutions to distinct problems.
11 pages, 3 figures
References in corpus (31)
- Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
- Updated Core Libraries of the ALPS Project
- Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
- Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
- Variational Benchmarks for Quantum Many-Body Problems
- Discrete Lehmann representation of imaginary time Green's functions
- Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
- Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
- Multipoint correlation functions: spectral representation and numerical evaluation
- Algorithmic Matsubara Integration for Hubbard-like models
- Sparse Modeling in Quantum Many-Body Problems
- Learning tensor networks with tensor cross interpolation: new algorithms and libraries
- Real-frequency Diagrammatic Monte Carlo at Finite Temperature
- A Tensor Train Continuous Time Solver for Quantum Impurity Models
- libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
- Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
- Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
- Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
- Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
- Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
- Two-particle calculations with quantics tensor trains: Solving the parquet equations
- Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
- Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis
- Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
- Spectral representation of Matsubara n-point functions: Exact kernel functions and applications
- Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
- Pairing susceptibility of the two-dimensional Hubbard model in the thermodynamic limit
- Discrete Lehmann representation of three-point functions
- cppdlr: Imaginary time calculations using the discrete Lehmann representation
- Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
- Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion