Stochastic pole expansion method

Abstract

In this paper, we propose a new analytic continuation method to extract real frequency spectral functions from imaginary frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara Green's function and a stochastic sampling procedure is utilized to optimize the amplitudes and locations of poles. In order to capture narrow peaks and sharp band edges in the spectral functions, a constrained sampling algorithm and a self-adaptive sampling algorithm are developed. To demonstrate the usefulness and performance of the new method, we at first apply it to study the spectral functions of representative fermionic and bosonic correlators. Then we employ this method to tackle the analytic continuation problems of matrix-valued Green's functions. The synthetic Green's functions, as well as realistic correlation functions from finite temperature quantum many-body calculations, are used as input. The benchmark results demonstrate that this method is capable of reproducing most of the key characteristics in the spectral functions. The sharp, smooth, and multi-peak features in both low-frequency and high-frequency regions of spectral functions could be accurately resolved, which overcomes one of the main limitations of the traditional maximum entropy method. More importantly, it exhibits excellent robustness with respect to noisy and incomplete input data. The causality of spectral function is always satisfied even in the presence of sizable noises. As a byproduct, this method could derive a fitting formula for the Matsubara data, which provides a compact approximation to the many-body Green's functions. Hence, we expect that this new method could become a pivotal workhorse for numerically analytic continuation and be broadly useful in many applications.

arXiv comment26 pages, 20 figures

References in corpus (61)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• The GW method
• Continuous-time Monte Carlo methods for quantum impurity models
• Electrodynamics of Correlated Electron Materials
• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• The AAA algorithm for rational approximation
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Nevanlinna Analytical Continuation
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Constrained sampling method for analytic continuation
• Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
• Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Artificial Neural Network Approach to the Analytic Continuation Problem
• Numerical analytic continuation: Answers to well-posed questions
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Analytic continuation via domain-knowledge free machine learning
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Analytic continuation by averaging Padé approximants
• Analytical continuation of imaginary axis data for optical conductivity
• Charmonium spectra at finite temperature from QCD sum rules with the maximum entropy method
• Analytical continuation of imaginary axis data using maximum entropy
• Pairing Glue in the Two Dimensional Hubbard Model
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Overcomplete compact representation of two-particle Green's functions
• Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation
• $i$QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Padé approximants for improved finite-temperature spectral functions in the numerical renormalization group
• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
• Maximum Entropy Analytic Continuation for Spectral Functions with Non-Positive Spectral Weight
• Continuous-Time Quantum Monte Carlo and Maximum Entropy Approach to an Imaginary-Time Formulation of Strongly Correlated Steady-State Transport
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Fermi liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
• Maximum Quantum Entropy Method
• $\text{TRIQS}/\text{SOM}$: Implementation of the Stochastic Optimization Method for Analytic Continuation
• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• Extending the average spectrum method: Grid points sampling and density averaging
• Ultralong-range order in the Fermi-Hubbard model with long-range interactions
• Bosonic Nevanlinna Analytic Continuation
• Continuous matrix product operator approach to finite temperature quantum states
• A Maximum Entropy Method of Obtaining Thermodynamic Properties from Quantum Monte Carlo Simulations
• Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited
• Analytic continuation average spectrum method for quantum liquids
• ACFlow: An open source toolkit for analytical continuation of quantum Monte Carlo data
• A comparison between methods of analytical continuation for bosonic functions
• Fast and Efficient Stochastic Optimization for Analytic Continuation
• Noise Enhanced Neural Networks for Analytic Continuation
• Maximum entropy analytic continuation for frequency-dependent transport coefficients with non-positive spectral weight
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• Two-particle Correlation Functions in Cluster Perturbation Theory: Hubbard Spin Susceptibilities
• Training biases in machine learning for the analytic continuation of quantum many-body Green's functions
• Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data
• Parameter-free analytic continuation for quantum many-body calculations

Cited by in corpus (7)

• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• Autoencoder-based analytic continuation method for strongly correlated quantum systems
• The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem