Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions

Abstract

We systematically generate the perturbative expansion for the two-particle spin susceptibility in the Feynman diagrammatic formalism and apply this expansion to a model system - the single-band Hubbard model on a square lattice. We make use of algorithmic Matsubara integration (AMI) [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019)] to analytically evaluate Matsubara frequency summations, allowing us to symbolically impose analytic continuation to the real frequency axis. We minimize our computational expense by applying graph invariant transformations [Amir Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 101, 125109 (2020)]. We highlight extensions of the random-phase approximation and T-matrix methods that, due to AMI, become tractable. We present results for weak interaction strength where the direct perturbative expansion is convergent, and verify our results on the Matsubara axis by comparison to other numerical methods. By examining the spin susceptibility as a function of real-frequency via an order-by-order expansion we can identify precisely what role higher order corrections play on spin susceptibility and demonstrate the utility and limitations of our approach.

References in corpus (41)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Spin waves and electronic interactions in La2CuO4
• Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
• Meron-Cluster Solution of Fermion Sign Problems
• Progress in Neutron Scattering Studies of Spin Excitations in High-Tc Cuprates
• Feynman diagrams versus Fermi-gas Feynman emulator
• Anomalous High-Energy Spin Excitations in La2CuO4
• Diagrammatic Monte Carlo
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Diagrammatic Monte Carlo for Correlated Fermions
• Pseudogap and antiferromagnetic correlations in the Hubbard model
• Strange metallicity in the doped Hubbard model
• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Updated Core Libraries of the ALPS Project
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Implementation of the Maximum Entropy Method for Analytic Continuation
• 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
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• The self-consistent Dyson equation and self-energy functionals: failure or new opportunities?
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• Algorithmic Matsubara Integration for Hubbard-like models
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Superconducting Fluctuations in the Normal State of the Two-Dimensional Hubbard Model
• Is there spin-charge separation in the 2D Hubbard and t-J models at low electronic densities?
• Real-frequency Diagrammatic Monte Carlo at Finite Temperature
• Origin of the high-energy charge excitations observed by resonant inelastic x-ray scattering in cuprate superconductors
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Magnetic Susceptibility and Simulated Neutron Signal in the 2D Hubbard Model
• Enhancement of Spin Susceptibility near Charge-Ordering Transition in a Two-Dimensional Extended Hubbard Model
• opendf - an implementation of the dual fermion method for strongly correlated systems
• Perturbation expansion for 2-D Hubbard model
• Counting Feynman diagrams via many-body relations
• Fluctuation diagnostics of the finite temperature quasi-antiferromagnetic regime of the 2D Hubbard model
• Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

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• Homotopic Action: A Pathway to Convergent Diagrammatic Theories
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Electrical conductivity in the Hubbard model: orbital effects of magnetic field
• Real-frequency response functions at finite temperature
• Charge fluctuations, hydrodynamics and transport in the square-lattice Hubbard model
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• 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
• One- and two-particle properties of the weakly interacting two-dimensional Hubbard model in proximity to the van Hove singularity
• Pairing susceptibility of the two-dimensional Hubbard model in the thermodynamic limit
• 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
• All electron GW with linearized augmented plane waves for metals and semiconductors
• Computation Kernel for Feynman Diagrams