Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis
arXiv:2211.02453 · doi:10.1103/PhysRevB.107.115151
Abstract
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but complex renormalization shift. The complex shift acts as a regularization parameter for the numerical integration of otherwise sharp functions. This results in an exponential speed up of stochastic numerical integration at the expense of evaluating additional counter-term diagrams. We provide proof of concept calculations within a difficult limit of the half-filled 2D Hubbard model on a square lattice.
References in corpus (27)
- Continuous-time Monte Carlo methods for quantum impurity models
- The Hubbard Model
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- The Hubbard model: A computational perspective
- Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
- Diagrammatic Monte Carlo
- Diagrammatic Monte Carlo for Correlated Fermions
- Nevanlinna Analytical Continuation
- Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
- Updated Core Libraries of the ALPS Project
- Implementation of the Maximum Entropy Method for Analytic Continuation
- Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
- Artificial Neural Network Approach to the Analytic Continuation Problem
- Analytic continuation via domain-knowledge free machine learning
- Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
- Analytic continuation by averaging Padé approximants
- Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
- Algorithmic Matsubara Integration for Hubbard-like models
- Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
- Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
- 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
- Real-frequency response functions at finite temperature
- Diagrammatic Monte Carlo Method for Impurity Models with General Interactions and Hybridizations
- Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
- LIBAMI: Implementation of Algorithmic Matsubara Integration
- One- and two-particle properties of the weakly interacting two-dimensional Hubbard model in proximity to the van Hove singularity
Cited by in corpus (5)
- Real-frequency quantum field theory applied to the single-impurity Anderson model
- Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion
- Computation Kernel for Feynman Diagrams
- An explicit formula for perturbation theory at any order with infinitely many perturbations
- Majorana Diagrammatics for Quantum Spin-1/2 Models