Analytic continuation of quantum Monte Carlo data. Stochastic sampling method

We apply Bayesian inference to the analytic continuation of quantum Monte Carlo (QMC) data from the imaginary axis to the real axis. Demanding a proper functional Bayesian formulation of any analytic continuation method leads naturally to the stochastic sampling method (StochS) as the Bayesian method with the simplest prior, while it excludes the maximum entropy method and Tikhonov regularization. We present a new efficient algorithm for performing StochS that reduces computational times by orders of magnitude in comparison to earlier StochS methods. We apply the new algorithm to a wide variety of typical test cases: spectral functions and susceptibilities from DMFT and lattice QMC calculations. Results show that StochS performs well and is able to resolve sharp features in the spectrum.