Constraints from anti-unitary 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 anti-unitary 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.