Robust analytic continuation combining the advantages of the sparse modeling approach and Padé approximation
arXiv:2109.08370 · doi:10.1103/PhysRevB.105.035139
Abstract
Analytic continuation (AC) from the imaginary-time Green's function to the spectral function is a crucial process for numerical studies of the dynamical properties of quantum many-body systems. This process, however, is an ill-posed problem; that is, the obtained spectrum is unstable against the noise of the Green's function. Though several numerical methods have been developed, each of them has its own advantages and disadvantages. The sparse modeling (SpM) AC method, for example, is robust against the noise of the Green's function but suffers from unphysical oscillations in the low-energy region. We propose a new method that combines the SpM AC with the Padé approximation. This combination, called SpM-Padé, inherits robustness against noise from SpM and low-energy accuracy from Padé, compensating for the disadvantages of each. We demonstrate that the SpM- Padé method yields low-variance and low-biased results with almost the same computational cost as that of the SpM method.
arXiv comment8 pages, 6 figures (proofread; changed text color, fixed some words)
References in corpus (26)
- Continuous-time Monte Carlo methods for quantum impurity models
- A continuous-time solver for quantum impurity models
- TRIQS: A Toolbox for Research on Interacting Quantum Systems
- Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
- Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
- Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
- Updated Core Libraries of the ALPS Project
- Constrained sampling method for analytic continuation
- Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data
- Artificial Neural Network Approach to the Analytic Continuation Problem
- Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
- Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
- Analytic continuation via domain-knowledge free machine learning
- Spectral Reconstruction with Deep Neural Networks
- Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
- Sparse Modeling in Quantum Many-Body Problems
- Overcomplete compact representation of two-particle Green's functions
- Solving the Bethe-Salpeter equation with exponential convergence
- Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors
- SpM: Sparse modeling tool for analytic continuation of imaginary-time Green's function
- Path-integral Monte Carlo method for the local Z_2 Berry phase
- DCore: Integrated DMFT software for correlated electrons
- Measuring Berry curvature with quantum Monte Carlo
- Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain
- Modified Pade approach for analytic continuation: Application to the zero-gap Kondo lattice model
- Spectral properties of heterostructures containing half-metallic ferromagnets in the presence of local many-body correlations