Understand
I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential.
- The representation is free of the "sign problem" irrespective of population imbalance, mass imbalance, and to a degree, sign of the interaction strength.
- This property is in sharp contrast with the analogous three-dimensional two-component interacting Fermi gas, which exhibits a sign problem in the case of unequal masses, chemical potentials, and repulsive interactions.
- The one-dimensional system is believed to exhibit many phenomena in common with its three-dimensional counterpart, including an analog of the BCS-BEC crossover, and nonperturbative universal few- and many-body physics at scattering lengths much larger than the range of interaction, making the theory an interesting candidate for numerical study.