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

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio 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.

Polarization contributions to the spin dependence of the effective interaction in neutron matter.

We calculate the modification of the effective interaction of particles on the Fermi surface due to polarization contributions, with particular attention to spin-dependent forces. In addition to the standard spin-spin, tensor, and spin-orbit forces, spin nonconserving effective interactions are induced by screening in the particle-hole channels. Furthermore, a novel long-wavelength tensor force is generated. We compute the polarization contributions to second order in the low-momentum interaction V(low k) and find that the medium-induced spin-orbit interaction leads to a reduction of the 3P2 pairing gap for neutrons in the interior of neutron stars.