Fast and Efficient Stochastic Optimization for Analytic Continuation

Abstract

The analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM) as a more accessible variant of the stochastic optimization method introduced by Mishchenko et al. and benchmark the resulting spectra with those obtained by the standard Maximum Entropy method for three representative test cases, in- cluding data taken from studies of the two-dimensional Hubbard model. We generally find that our FESOM approach gives spectra similar to the Maximum Entropy results. In particular, while the Maximum Entropy method gives superior results when the quality of the data is strong, we find that FESOM is able to resolve fine structure with more detail when the quality of the data is poor. In addition, because of its stochastic nature, the method provides detailed information on the frequency dependent uncertainty of the resulting spectra, while the Maximum Entropy method does so only for the spectral weight integrated over a finite frequency region. We therefore believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used Maximum Entropy method especially for data with poor quality.

11 pages, 7 figures

References in corpus (7)

• Quantum Cluster Theories
• The pseudogap: friend or foe of high Tc?
• Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Phase Diagram of the Hubbard Model: Beyond the Dynamical Mean Field
• Spectral Analysis by the Method of Consistent Constraints

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• Sparse Modeling in Quantum Many-Body Problems
• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
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• Bayesian parametric analytic continuation of Green's functions
• Stochastic pole expansion method
• Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• Analytic Continuation of Noisy Data Using Adams Bashforth ResNet
• The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem
• A Parameter-Free Differential Evolution Algorithm for the Analytic Continuation of Imaginary Time Correlation Functions