BAYESIAN-INFERENCE AND THE ANALYTIC CONTINUATION OF IMAGINARY-TIME QUANTUM MONTE-CARLO DATA

We present a way to use Bayesian statistical inference and the princip le of maximum entropy to analytically continue imaginary-time quantum Monte Carlo data. We supply the details that are lacking in the semina l literature but are important for the motivated reader to understand the assumptions and approximations embodied in these methods. First, w e summarize the general relations between quantum correlation function s and spectral densities. We then review the basic principles, formali sm, and philosophy of Bayesian inference and discuss the application o f this approach in the context of the analytic continuation problem. N ext, we present a detailed case study for the symmetric, infinite-dime nsion Anderson Hamiltonian. We chose this Hamiltonian because the qual itative features of its spectral density are well established and beca use a particularly convenient algorithm exists to produce the imaginar y-time Green's function data. Shown are all the intermediate steps of data and solution qualification. The importance of careful data prepar ation and error propagation in the analytic continuation is discussed in the context of this example. Then, we review the different physical systems and physical quantities to which these, or related, procedure s have been applied. Finally, we describe other features concerning th e application of our methods, their possible improvement, and areas fo r additional study.