Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure

Abstract

We present a general method to optimize the evaluation of Feynman diagrammatic expansions, which requires the automated symbolic assignment of momentum/energy conserving variables to each diagram. With this symbolic representation, we utilize the pole structure of each diagram to automatically sort the Feynman diagrams into groups that are likely to contain nearly equal or nearly cancelling diagrams, and we show that for some systems this cancellation is exact. This allows for a potentially massive cancellation during the numerical integration of internal momenta variables, leading to an optimal suppression of the `sign problem' and hence reducing the computational cost. Although we define these groups using a frequency space representation, the equality or cancellation of diagrams within the group remains valid in other representations such as imaginary time used in standard diagrammatic Monte Carlo. As an application of the approach we apply this method, combined with algorithmic Matsubara integration (AMI) [Phys. Rev. B 99, 035120 (2019)] and Monte Carlo methods, to the Hubbard model self-energy expansion on a 2D square lattice up to sixth order which we evaluate and compare with existing benchmarks.

References in corpus (34)

• Quantum Cluster Theories
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Worm algorithms for classical statistical models
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Meron-Cluster Solution of Fermion Sign Problems
• Feynman diagrams versus Fermi-gas Feynman emulator
• Diagrammatic Monte Carlo
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Diagrammatic Monte Carlo for Correlated Fermions
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Implementation of the Maximum Entropy Method for Analytic Continuation
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model
• Conserving approximations for the attractive Holstein and Hubbard models
• Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• Equation of State of the Fermionic 2D Hubbard Model
• Diagrammatic Monte Carlo for Dual Fermions
• Algorithmic Matsubara Integration for Hubbard-like models
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Iterated perturbation theory for the attractive Holstein and Hubbard models
• Fourth-Order Perturbation Theory for the Half-Filled Hubbard Model in Infinite Dimensions
• Real-frequency Diagrammatic Monte Carlo at Finite Temperature
• Updated Core Libraries of the ALPS Project
• Perturbation expansion for 2-D Hubbard model
• Counting Feynman diagrams via many-body relations
• Fourth Order Perturbation Theory for Normal Selfenergy in Repulsive Hubbard Model
• Orthogonal Tree Decompositions of Graphs

Cited by in corpus (21)

• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Charge transport in the Hubbard model at high temperatures: triangular versus square lattice
• Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
• Renormalized perturbation theory at large expansion orders
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Numerically Exact Generalized Green's Function Cluster Expansions for Electron-Phonon Problems
• Electrical conductivity in the Hubbard model: orbital effects of magnetic field
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo
• Charge fluctuations, hydrodynamics and transport in the square-lattice Hubbard model
• Real-frequency response functions at finite temperature
• LIBAMI: Implementation of Algorithmic Matsubara Integration
• 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
• Pairing susceptibility of the two-dimensional Hubbard model in the thermodynamic limit
• Photoemission "experiments" on holographic lattices
• Solving the Bethe-Salpeter Equation in Real Frequencies at Finite Temperature
• Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System
• Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion
• Computation Kernel for Feynman Diagrams