Green's functions from real-time bold-line Monte Carlo

We present two methods for computing two-time correlation functions or Green's functions from real-time bold-line continuous-time quantum Monte Carlo. One method is a formally exact generalized auxiliary lead formalism by which spectral properties may be obtained from single-time observables. The other involves the evaluation of diagrams contributing to two-time observables directly on the Keldysh contour. Additionally, we provide a detailed description of the bold-line Monte Carlo method. Our methods are general and numerically exact, and able to reliably resolve high-energy features such as band edges. We compare the spectral functions obtained from real-time methods to analytically continued spectral functions obtained from imaginary-time Monte Carlo, thus probing the limits of analytic continuation.