Nevanlinna Analytical Continuation

Abstract

Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one-to-one to experimentally measurable real-frequency spectral functions. However, due to the bad conditioning of the continuation transform from imaginary to real frequencies, established methods tend to either wash out spectral features at high frequencies or produce spectral functions with unphysical negative parts. Here, we show that explicitly respecting the analytic `Nevanlinna' structure of the Green's function leads to intrinsically positive and normalized spectral functions, and we present a continued fraction expansion that yields all possible functions consistent with the analytic structure. Application to synthetic trial data shows that sharp, smooth, and multi-peak data is resolved accurately. Application to the band structure of silicon demonstrates that high energy features are resolved precisely. Continuations in a realistic correlated setup reveal additional features that were previously unresolved. By substantially increasing the resolution of real frequency calculations our work overcomes one of the main limitations of finite-temperature quantum simulations.

References in corpus (34)

• Separable Dual Space Gaussian Pseudo-potentials
• Continuous-time Monte Carlo methods for quantum impurity models
• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• \textit{Ab Initio} Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter
• Excitation spectrum of a supersolid
• A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Ab-initio low-energy dynamics of superfluid and solid 4He
• Updated Core Libraries of the ALPS Project
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• 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
• Implementation of the Maximum Entropy Method for Analytic Continuation
• Numerical analytic continuation: Answers to well-posed questions
• Antiferromagnetism and the gap of a Mott insulator: Results from analytic continuation of the self-energy
• Numerical analytic continuation of Euclidean data
• Identifying the maximum entropy method as a special limit of stochastic analytic continuation
• Analytic continuation by averaging Padé approximants
• Analytical continuation of imaginary axis data for optical conductivity
• Spectral weight function for the half-filled Hubbard model: a singular value decomposition approach
• Quasiparticle Properties of the Superconducting State of the Two Dimensional Hubbard Model
• Local Hamiltonians for quantitative Green's function embedding methods
• Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory
• Correlation effects and collective excitations in bosonic bilayers: role of quantum statistics, superfluidity and dimerization transition
• Padé approximants for improved finite-temperature spectral functions in the numerical renormalization group
• Maximum Quantum Entropy Method
• $\text{TRIQS}/\text{SOM}$: Implementation of the Stochastic Optimization Method for Analytic Continuation
• Magnetic Susceptibility and Simulated Neutron Signal in the 2D Hubbard Model
• One particle spectral function and analytic continuation for many-body implementation in the EMTO method
• Bryan's Maximum Entropy Method -- diagnosis of a flawed argument and its remedy
• Bayesian parametric analytic continuation of Green's functions
• Analytic continuation with Padé decomposition

Cited by in corpus (71)

• The Hubbard model: A computational perspective
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Quantum Monte Carlo in the steady-state
• Large Exciton Binding Energy in the Bulk van der Waals Magnet CrSBr
• Comparing self-consistent GW and vertex corrected G0W0 (G0W0Γ) accuracy for molecular ionization potentials
• Relativistic Self-Consistent $GW$: Exact Two-Component Formalism with One-Electron Approximation for Solids
• A Tensor Train Continuous Time Solver for Quantum Impurity Models
• Iterative subspace algorithms for finite-temperature solution of Dyson equation
• Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Bosonic Nevanlinna Analytic Continuation
• Non-perturbative strong coupling at timelike momenta
• Analytic continuation from limited noisy Matsubara data
• A fast time domain solver for the equilibrium Dyson equation
• ACFlow: An open source toolkit for analytical continuation of quantum Monte Carlo data
• The QCD moat regime and its real-time properties
• Learned Optimizers for Analytic Continuation
• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
• Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators
• Fourier-Matsubara series expansion for imaginary-time correlation functions
• Excitations and spectra from equilibrium real-time Green's functions
• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
• Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
• 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
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Stochastic pole expansion method
• Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Minimal pole representation for spectral functions
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Nevanlinna.jl: A Julia implementation of Nevanlinna analytic continuation
• Equivariant neural network for Green's functions of molecules and materials
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Maximum entropy analytic continuation of anomalous self-energies
• Dual formulation of the maximum entropy method applied to analytic continuation of quantum Monte Carlo data
• TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data
• SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions
• Modified $GW$ Method in Electronic Systems
• Analytic continuation of multipoint correlation functions
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Trie-based ranking of quantum many-body states
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Supersolid Phase in the Diluted Holstein Model
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• Denoising of Imaginary Time Response Functions with Hankel projections
• Parameter-free analytic continuation for quantum many-body calculations
• Heating and cooling in self-consistent many-body simulations
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• Physically interpretable approximations of many-body spectral functions
• Orbital Magnetic Field Driven Metal-Insulator Transition in Strongly Correlated Electron Systems
• High-temperature series expansion of the dynamic Matsubara spin correlator
• Autoencoder-based analytic continuation method for strongly correlated quantum systems
• Nevanlinna Analytic Continuation for Migdal-Eliashberg Theory
• Natural orbital impurity solver for real-frequency properties at finite temperature
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Multi-orbital dynamical mean-field theory with a complex-time solver
• Algorithm for computing perturbation series of dynamical mean field theory
• Nevanlinna-Pick interpolation from uncertain data
• Determination of Fermi surface by charge density correlations
• The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem
• Engineering correlated Dirac fermions and flat bands on SiC with transition-metal adatom lattices
• Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism