Cross Validation in the Stochastic Analytic Continuation (SAC) Method

Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experiments. Recent developments of the SAC method have allowed for spectral functions with sharp features, e.g. narrow peaks and divergent edges, to be resolved with unprecedented fidelity. In these newly developed "constrained" sampling methods, parameters, such as a spectral edge locations and quasi-particle peak amplitudes, must be optimized using a statistical criterion. In this work, we borrow from the machine learning and statistics literature, and implement a cross-validation technique to provide unbiased support for previously proposed simple optimization criteria. We show examples using imaginary-time data generated by QMC simulations and from synthetic spectra.