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Title: Fast and Efficient Stochastic Optimization for Analytic Continuation

Abstract

In this 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. [Phys. Rev. B 62, 6317 (2000)], and we benchmark the resulting spectra with those obtained by the standard maximum entropy method for three representative test cases, including data taken from studies of the two-dimensional Hubbard model. Genearally, we find that our FESOM approach yields spectra similar to the maximum entropy results. In particular, while the maximum entropy method yields 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. Therefore, we believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used maximum entropy method, especiallymore » for data of poor quality.« less

Authors:
 [1];  [1];  [1];  [1];  [2];  [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1336574
Alternate Identifier(s):
OSTI ID: 1327072
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 94; Journal Issue: 12; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Bao, Feng, Zhang, Guannan, Webster, Clayton G, Tang, Yanfei, Scarola, Vito, Summers, Michael Stuart, and Maier, Thomas A. Fast and Efficient Stochastic Optimization for Analytic Continuation. United States: N. p., 2016. Web. doi:10.1103/PhysRevB.94.125149.
Bao, Feng, Zhang, Guannan, Webster, Clayton G, Tang, Yanfei, Scarola, Vito, Summers, Michael Stuart, & Maier, Thomas A. Fast and Efficient Stochastic Optimization for Analytic Continuation. United States. doi:10.1103/PhysRevB.94.125149.
Bao, Feng, Zhang, Guannan, Webster, Clayton G, Tang, Yanfei, Scarola, Vito, Summers, Michael Stuart, and Maier, Thomas A. Wed . "Fast and Efficient Stochastic Optimization for Analytic Continuation". United States. doi:10.1103/PhysRevB.94.125149. https://www.osti.gov/servlets/purl/1336574.
@article{osti_1336574,
title = {Fast and Efficient Stochastic Optimization for Analytic Continuation},
author = {Bao, Feng and Zhang, Guannan and Webster, Clayton G and Tang, Yanfei and Scarola, Vito and Summers, Michael Stuart and Maier, Thomas A},
abstractNote = {In this 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. [Phys. Rev. B 62, 6317 (2000)], and we benchmark the resulting spectra with those obtained by the standard maximum entropy method for three representative test cases, including data taken from studies of the two-dimensional Hubbard model. Genearally, we find that our FESOM approach yields spectra similar to the maximum entropy results. In particular, while the maximum entropy method yields 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. Therefore, we believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used maximum entropy method, especially for data of poor quality.},
doi = {10.1103/PhysRevB.94.125149},
journal = {Physical Review B},
number = 12,
volume = 94,
place = {United States},
year = {2016},
month = {9}
}

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