In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, highly doped FeSe reverses 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.
