Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation

Abstract

The reconstruction of spectral functions from Euclidean correlation functions is a well-known, yet ill-posed inverse problem in the fields of many-body and high-energy physics. In this paper, we present a comprehensive investigation of two recently developed analytic continuation methods, namely stochastic pole expansion and Nevanlinna analytic continuation, for extracting spectral functions from mock lattice QCD data. We examine a range of Euclidean correlation functions generated by representative models, including the Breit-Wigner model, the Gaussian mixture model, the resonance-continuum model, and the bottomonium model. Our findings demonstrate that the stochastic pole expansion method, when combined with the constrained sampling algorithm and the self-adaptive sampling algorithm, successfully recovers the essential features of the spectral functions and exhibits excellent resilience to noise of input data. In contrast, the Nevanlinna analytic continuation method suffers from numerical instability, often resulting in the emergence of spurious peaks and significant oscillations in the high-energy regions of the spectral functions, even with the application of the Hardy basis function optimization algorithm.

arXiv comment14 pages, 8 figures

References in corpus (42)

• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• $J/\psi$ and ${\eta }_c$ in the Deconfined Plasma from Lattice QCD
• Behavior of Charmonium Systems after Deconfinement
• The Search for the Quark-Gluon Plasma
• Thermal dilepton rate and electrical conductivity: An analysis of vector current correlation functions in quenched lattice QCD
• Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD
• Lattice QCD and heavy ion collisions: a review of recent progress
• A novel Bayesian approach to spectral function reconstruction
• Charmonium properties in hot quenched lattice QCD
• Quarkonium correlators and spectral functions at zero and finite temperature
• Charmonium at high temperature in two-flavor QCD
• Heavy Quarkonium in Extreme Conditions
• Charmonium at finite temperature in quenched lattice QCD
• A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
• What happens to the Upsilon and eta_b in the quark-gluon plasma? Bottomonium spectral functions from lattice QCD
• 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
• Constrained sampling method for analytic continuation
• The bottomonium spectrum at finite temperature from $N_f=2+1$ lattice QCD
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Numerical analytic continuation of Euclidean data
• Heavy-Quark Diffusion in the Quark-Gluon Plasma
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Spectral Reconstruction with Deep Neural Networks
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Analytic continuation by averaging Padé approximants
• Charmonium spectral functions with the variational method in zero and finite temperature lattice QCD
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Padé approximants for improved finite-temperature spectral functions in the numerical renormalization group
• Rethinking the ill-posedness of the spectral function reconstruction -- why is it fundamentally hard and how Artificial Neural Networks can help
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Stochastic reconstructions of spectral functions: Application to lattice QCD
• Extending the average spectrum method: Grid points sampling and density averaging
• Bosonic Nevanlinna Analytic Continuation
• ACFlow: An open source toolkit for analytical continuation of quantum Monte Carlo data
• Bayesian inference of real-time dynamics from lattice QCD
• Stochastic pole expansion method
• Nevanlinna.jl: A Julia implementation of Nevanlinna analytic continuation

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