Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference

TL;DR

This paper introduces a Bayesian-based algorithm for analytic continuation of quantum Monte Carlo data, providing a principled way to estimate energy spectra without ad-hoc regularization choices.

Contribution

It develops a novel Bayesian inference method for analytic continuation that explicitly calculates weighted averages over spectra, avoiding arbitrary regularization parameters.

Findings

Algorithm successfully applied to quantum Monte Carlo data

Results compare favorably with maximum entropy methods

Provides a distribution of spectra as a function of regularization

Abstract

We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad-hoc assumptions introduced in similar algortihms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum entropy calculation.