Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference

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.

References in corpus (2)

• The ALPS project release 1.3: open source software for strongly correlated systems
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations

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