Constraints from antiunitary symmetries on phase diagrams of sign problem free models

A powerful way to guarantee the absence of a sign problem in determinantal quantum Monte Carlo simulations is imposing a particular type of antiunitary symmetries. It is shown that these same symmetries give rise to constraints on correlation functions, which can be used to identify local operators whose correlations upper bound those of a large class of physically relevant operators, including for example superconducting order parameters. Our results also help understand why it is difficult to realize generic finite-momentum orders in sign problem free models.