Imaginary Polarization as a Way to Surmount the Sign Problem inAb InitioCalculations of Spin-Imbalanced Fermi Gases

Abstract

From ultracold atoms to quantum chromodynamics, reliable abinitio studies of strongly interacting fermions require numerical methods, typically in some form of quantum MonteCarlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those abinitio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.