Analytic continuation of Matsubara Green's functions

Abstract

Obtaining dynamical characteristics of lattice field models amounts to analytic continuation of the simulated Matsubara Green's functions into the real frequency domain. This is in general an ill-posed problem with the statistical errors and the correlations in the simulation data imposing additional difficulties on its solution. We present a technique to extract dynamical correlation functions, using singular value decomposition. Prior information on the range of support of the expected solution and optimal sampling of the simulation data are incorporated in the analytic continuation procedure. Results are presented for the spectrum, density of states and dynamical spin susceptibility in the Hubbard and Heisenberg models. A generalisation of the method to the spectrum of QCD is proposed.