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Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation.

Dominic Bergeron1, A-M S Tremblay1,2

  • 1Département de physique, Regroupement Québécois sur les Matériaux de Pointe, Université de Sherbrooke, Québec, Canada.

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Maximum entropy analytic continuation, a key quantum physics method, is optimized for speed and accuracy. This research introduces a user-friendly software for this complex numerical problem, improving computational efficiency and reliability.

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Area of Science:

  • Quantum computational physics
  • Computational physics
  • Bayesian inference

Background:

  • Analytic continuation of imaginary time/frequency data is crucial in quantum computational physics.
  • This procedure is numerically ill-conditioned and challenging.
  • The maximum entropy method (MEM) is the standard approach but lacks optimized, user-friendly software.

Purpose of the Study:

  • To develop a highly optimized and user-friendly software for maximum entropy analytic continuation.
  • To improve the accuracy and computational speed of analytic continuation.
  • To provide robust diagnostics for assessing the reliability of results.

Main Methods:

  • Developed novel numerical approximations for computational complexity nearly independent of temperature and spectrum shape.
  • Introduced a robust method for selecting the entropy weight (α) based on a consistency condition and χ² analysis.
  • Implemented several diagnostics for result reliability assessment.

Main Results:

  • Achieved quantitative accuracy and computational efficiency, even with complex spectral functions like sharp Drude peaks.
  • Identified clear information- and noise-fitting regimes through χ² behavior analysis.
  • Demonstrated performance with benchmarks and a physical simulation for fermions, bosons, and response functions.

Conclusions:

  • The presented approach significantly enhances the speed and accuracy of maximum entropy analytic continuation.
  • The open-source, user-friendly software addresses the need for a dedicated, optimized tool in the field.
  • The developed diagnostics and methods improve the reliability and interpretability of analytic continuation results.