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

TL;DR

This paper explores using imaginary polarization in quantum Monte Carlo calculations to overcome the sign problem in nonrelativistic spin-imbalanced Fermi gases, enabling phase diagram studies.

Contribution

It introduces a novel approach of using complex chemical potentials with imaginary polarization to bypass the sign problem in nonrelativistic fermionic systems.

Findings

Sign problem is avoided with imaginary polarization in nonrelativistic systems.

Mean-field analysis of phase diagram with imaginary polarization conducted.

First step towards applying analytic continuation methods in nonrelativistic quantum simulations.

Abstract

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.