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From ultracold atoms to quantum chromodynamics, reliable ab initio studies ofstrongly interacting fermions require numerical methods, typically in some formof quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems atfinite density (spin polarization) generally have a sign problem, such thatthose ab initio calculations are impractical. It is well-known, however, thatin the relativistic case imaginary chemical potentials solve this problem,assuming the data can be analytically continued to the real axis. Is thisfeasible for nonrelativistic systems? Are the interesting features of the phasediagram accessible in this manner? By introducing complex chemical potentials,for real total particle number and imaginary polarization, the sign problem isavoided in the nonrelativistic case. To give a first answer to the abovequestions, we perform a mean-field study of the finite-temperature phasediagram of spin-1/2 fermions with imaginary polarization.

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases