Numerical analytic continuation of Euclidean data

Abstract

In this work we present a direct comparison of three different numerical analytic continuation methods: the Maximum Entropy Method, the Backus-Gilbert method and the Schlessinger point or Resonances Via Padé method. First, we perform a benchmark test based on a model spectral function and study the regime of applicability of these methods depending on the number of input points and their statistical error. We then apply these methods to more realistic examples, namely to numerical data on Euclidean propagators obtained from a Functional Renormalization Group calculation, to data from a lattice Quantum Chromodynamics simulation and to data obtained from a tight-binding model for graphene in order to extract the electrical conductivity.

32 pages, 19 figures

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• Recent Progress in QCD Condensate Evaluations and Sum Rules
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• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
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• Quantum algorithms for transport coefficients in gauge theories
• Spectral representation of lattice gluon and ghost propagators at zero temperature
• Spectrum of scalar and pseudoscalar glueballs from functional methods
• Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD
• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Reconstruction of smeared spectral function from Euclidean correlation functions
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Scattering amplitudes and contour deformations
• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Lattice Renormalization of Quantum Simulations
• Four-quark states from functional methods
• Spectral functions and critical dynamics of the $O(4)$ model from classical-statistical lattice simulations
• Reconstructing spectral functions via automatic differentiation
• Higher spin glueballs from functional methods
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Vector and Axial-Vector Mesons in Nuclear Matter
• Rethinking the ill-posedness of the spectral function reconstruction -- why is it fundamentally hard and how Artificial Neural Networks can help
• Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations
• Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions
• The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach
• Going to the light front with contour deformations
• Apparent convergence of Padé approximants for the crossover line in finite density QCD
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
• Fluctuating vector mesons in analytically continued FRG flow equations
• Inverse problems, real-time dynamics and lattice simulations
• Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
• Schwinger pair production from Padé-Borel reconstruction
• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
• Study for a model-independent pole determination of overlapping resonances
• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• Fermionic excitations at finite temperature and density
• Thermal properties of $\pi$ and $\rho$ meson
• First-principle quantum Monte-Carlo study of charge carrier mobility in organic molecular semiconductors
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• The analytic structure of three-point functions from contour deformations
• Quantum mean estimation for lattice field theory
• Real-time observables from Euclidean thermal correlation functions
• Euclidean thermal correlation functions in local QFT
• Universal collective modes from strong electronic correlations: Modified $1/{\mathcal{N}}_f$ theory with application to high-$T_c$ cuprates
• Dual formulation of the maximum entropy method applied to analytic continuation of quantum Monte Carlo data
• Static quark anti-quark interactions at non-zero temperature from lattice QCD
• Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball
• Extracting a model quark propagator's spectral density
• Bridging the gap between numerics and experiment in free standing graphene
• Glueballs from bound state equations
• Quarkonium Production in the QGP
• PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods
• Quenched glueball spectrum from functional equations