Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data

Area of Science:

• Computational Physics
• Data Science
• Quantum Many-Body Theory

Background:

• Analytical continuation is crucial for inferring real-frequency spectra from imaginary-time data.
• Ill-conditioned inverse problems, like analytical continuation, are highly sensitive to noise in input data.
• Noise in imaginary-time data significantly distorts inferred real-frequency spectra.

Purpose of the Study:

• To develop a robust data-science framework for stable analytical continuation.
• To mitigate the impact of noise on spectral function inference.
• To establish criteria for the accuracy of input data in spectral analysis.

Main Methods:

• Employed a modern regularization technique to filter noise from imaginary-time data.
• Reduced degrees of freedom to isolate signal from noise.
• Utilized minimal basis representation for stable spectral reconstruction.

Main Results:

• Achieved stable analytical continuation by effectively removing noise-dominant components.
• The method successfully infers real-frequency spectra with improved accuracy.
• Developed a tool to quantify necessary Monte Carlo data precision for spectral details.

Conclusions:

• The proposed data-science approach offers a stable solution for analytical continuation.
• This method enhances the reliability of spectral function analysis from noisy data.
• Provides a quantitative guide for experimental and computational data acquisition.