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We study the 2+1 dimensional XY model at nonzero chemical potential $\mu$ ondeformed integration manifolds, with the aim of alleviating its sign problem.We investigate several proposals for the deformations, and considerably improveon the severity of the sign problem with respect to standard reweightingapproaches. We present numerical evidence that the reduction of the signproblem is exponential both in $\mu^2$ and in the spatial volume. We alsopresent a new approach to the optimization procedure based on reweighting, thatsensibly reduces its computational cost.

Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations