Analytic continuation of quantum Monte Carlo data by stochastic analytical inference

Area of Science:

• Computational Physics
• Statistical Mechanics
• Quantum Many-Body Theory

Background:

• Analytic continuation is crucial for extracting physical observables from imaginary-time quantum Monte Carlo (QMC) data.
• Traditional methods often rely on ad hoc assumptions for regularization, introducing uncertainties.
• Bayesian inference offers a principled framework for handling inverse problems like analytic continuation.

Purpose of the Study:

• To present a novel algorithm for analytic continuation based strictly on Bayesian statistical inference.
• To provide an explicit expression for calculating weighted averages of energy spectra.
• To avoid and overcome the limitations of arbitrary regularization parameter choices in existing methods.

Main Methods:

• Developed an algorithm grounded in Bayesian statistical inference principles.
• Derived an explicit expression for weighted average calculation of energy spectra.
• Utilized standard Monte Carlo simulations for evaluation, obtaining the distribution function as a byproduct.

Main Results:

• The algorithm successfully performs analytic continuation of imaginary-time QMC data.
• It yields a weighted average over possible energy spectra, incorporating uncertainty quantification.
• The distribution function as a function of the regularization parameter is obtained intrinsically.

Conclusions:

• The proposed Bayesian algorithm offers a rigorous and assumption-free approach to analytic continuation.
• It provides a more reliable method for determining energy spectra compared to standard maximum-entropy calculations.
• This framework enhances the analysis of QMC data in various quantum systems.