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

Superconductivity and Nematic Fluctuations in a model of FeSe monolayers: A Determinant Quantum Monte Carlo Study