  In contrast to bulk FeSe, which exhibits nematic order and low temperature
superconductivity, atomic layers of FeSe reverse the situation, having high
temperature superconductivity appearing alongside a suppression of nematic
order. To investigate this phenomenon, we study a minimal electronic model of
FeSe, with interactions that enhance nematic fluctuations. This model is sign
problem free, and is simulated using determinant quantum Monte Carlo (DQMC). We
developed a DQMC algorithm with parallel tempering, which proves to be an
efficient source of global updates and allows us to access the region of strong
interactions. Over a wide range of intermediate couplings, we observe
superconductivity with an extended s-wave order parameter, along with enhanced,
but short ranged, $q=(0,0)$ ferro-orbital (nematic) order. These results are
consistent with approximate weak coupling treatments that predict that nematic
fluctuations lead to superconducting pairing. Surprisingly, in the parameter
range under study, we do not observe nematic long range order. Instead, at
stronger coupling an unusual insulating phase with $q=(\pi,\pi)$
antiferro-orbital order appears, which is missed by weak coupling
approximations.
