Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion

Abstract

We present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an $M$th-order diagram at inverse temperature $\beta$ and spectral width ${\omega }_{\max }$ from $\mathcal{O}((\beta {\omega }_{\max }{)}^{2M-1})$ for a direct quadrature to $\mathcal{O}(M(\log (\beta {\omega }_{\max }){)}^{M+1})$, with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multi-band impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca${}_2$RuO${}_4$, demonstrating the promise of the method for modeling realistic strongly correlated multi-band materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust black-box evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams.

References in corpus (80)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Continuous-time Monte Carlo methods for quantum impurity models
• A continuous-time solver for quantum impurity models
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• Continuous Time Quantum Monte Carlo method for fermions
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
• The coherence-incoherence crossover and the mass-renormalization puzzles in Sr2RuO4
• Excitonic Magnetism in Van Vleck-type d^4 Mott Insulators
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations
• TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials
• Strongly Correlated Superconductivity: a plaquette Dynamical mean field theory study
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Diagrammatic Monte Carlo
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Nature of the Mott transition in Ca2RuO4
• Anderson impurity model at finite Coulomb interaction U: generalized Non-crossing Approximation
• Spectral Properties of the Anderson Impurity Model, Comparison of Numerical Renormalization Group and Non--Crossing Approximation
• Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• NESSi: The Non-Equilibrium Systems Simulation package
• Magnetic couplings, optical spectra, and spin-orbit exciton in 5d electron Mott insulator Sr2IrO4
• Hallmarks of Hund's coupling in the Mott insulator Ca${}_2$RuO${}_4$
• Multitier self-consistent $GW$+EDMFT
• The Fermi surface of Sr2RuO4: spin-orbit and anisotropic Coulomb interaction effects
• Mixing of $t_{2g}$-$e_g$ orbitals in 4d and 5d transition metal oxides
• Learning Feynman Diagrams with Tensor Trains
• Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation
• Subband filling and Mott transition in Ca_{2-x}Sr_xRuO_4
• Spin-dependent Hedin's equations
• Electronic orders in multi-orbital Hubbard models with lifted orbital degeneracy
• Performance analysis of continuous-time solvers for quantum impurity models
• Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model
• Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
• Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
• Discrete Lehmann representation of imaginary time Green's functions
• Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Dynamics of screening in photo-doped Mott insulators
• Multi-band non-equilibrium GW+EDMFT formalism for correlated insulators
• Continuous-time Quantum Monte Carlo using Worm Sampling
• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems
• Lattice Energetics and Correlation-Driven Metal-Insulator Transitions: The Case of Ca${}_2$RuO${}_4$
• Magnetic Excitations in Spin-Orbit Coupled $d^4$ Mott Insulator on Square Lattice
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Multi-orbital Non-Crossing Approximation from maximally localized Wannier functions: the Kondo signature of copper phthalocyanine on Ag (100)
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation
• Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations
• Diagrammatic Monte Carlo study of the Fröhlich polaron dispersion in 2D and 3D
• Symmetric Improved Estimators for Continuous-time Quantum Monte Carlo
• 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
• Hund's coupling driven photo-carrier relaxation in the two-band Mott insulator
• Spectral functions of Sr${}_2$IrO${}_4$: theory versus experiment
• Low-Scaling Algorithm for the Random Phase Approximation using Tensor Hypercontraction with k-point Sampling
• Coupled charge and spin dynamics in a photo-excited Mott insulator
• A fast time domain solver for the equilibrium Dyson equation
• Sparse modeling of large-scale quantum impurity models with low symmetries
• Superconductivity in the Uniform Electron Gas: Irrelevance of Kohn-Luttinger Mechanism
• Metal-Insulator and Magnetic Phase Diagram of Ca${}_2$RuO${}_4$ from Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory
• Quantitative comparison of Anderson impurity solvers applied to transport in quantum dots
• Efficient construction of canonical polyadic approximations of tensor networks
• Low rank Green's function representations applied to dynamical mean-field theory
• A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
• Reliability of the one-crossing approximation in describing the Mott transition

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