Elucidating the interplay between non-stoquasticity and the sign problem

The sign problem is a key challenge in computational physics, encapsulating our inability to properly understand many important quantum many-body phenomena in physics, chemistry and the material sciences. Despite its centrality, the circumstances under which the problem arises or can be resolved as well as its interplay with the related notion of `non-stoquasticity' are often not very well understood. In this study, we make an attempt to elucidate the circumstances under which the sign problem emerges and to clear up some of the confusion surrounding this intricate computational phenomenon. To that aim, we make use of the recently introduced off-diagonal series expansion quantum Monte Carlo scheme with which we analyze in detail a number of examples that capture the essence of our results.