Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data
arXiv:2212.05475 · doi:10.1103/PhysRevB.107.085129
Abstract
Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still being developed. This paper explores a regularization method based on the repeated application of Tikhonov regularization under the discrepancy principle. The method can be readily implemented in any linear algebra package and gives results surprisingly close to the maximum entropy method (MaxEnt). We analyze the method in detail and demonstrate its connection to MaxEnt. In addition, we provide a straightforward method for estimating the noise level of QMC data, which is helpful for practical applications of the discrepancy principle when the noise level is not known reliably.
arXiv comment12 pages, 10 figures
References in corpus (20)
- Machine learning for many-body physics: The case of the Anderson impurity model
- A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
- Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
- Ab-initio low-energy dynamics of superfluid and solid 4He
- Constrained sampling method for analytic continuation
- Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
- Artificial Neural Network Approach to the Analytic Continuation Problem
- 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
- Analytic continuation via domain-knowledge free machine learning
- Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
- Analytic continuation by averaging Padé approximants
- Analytical continuation of imaginary axis data for optical conductivity
- Analytical continuation of imaginary axis data using maximum entropy
- Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
- The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
- Extending the average spectrum method: Grid points sampling and density averaging
- One particle spectral function and analytic continuation for many-body implementation in the EMTO method
- Fast and Efficient Stochastic Optimization for Analytic Continuation