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We study the sign problem in the Hubbard model on the hexagonal lattice awayfrom half-filling using the Lefschetz thimbles method. We identify the saddlepoints, reduce their amount, and perform quantum Monte Carlo (QMC) simulationsusing the holomorphic gradient flow to deform the integration contour incomplex space. Finally, the results are compared against exact diagonalization(ED). We show that the sign problem can be substantially weakened, even in theregime with low temperature and large chemical potential, where standard QMCtechniques exhibit an exponential decay of the average sign.

Taming the sign problem of the finite density Hubbard model via Lefschetz thimbles