Tan's contact and the phase distribution of repulsive Fermi gases: Insights from quantum chromodynamics noise analyses

Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to nonrelativistic Fermi gases with repulsive interactions. Using arguments similar to those previously applied to relativistic theories, we show that the analogous problem in nonrelativistic systems manifests itself naturally in Tan's contact as a nontrivial cancellation between terms with varied dependence on extensive thermodynamic quantities. We analyze that case under the assumption of a Gaussian phase distribution, which is supported by our Monte Carlo calculations and perturbative considerations. We further generalize these results to observables other than the contact, as well as to polarized systems and systems with fixed particle number. Our results are quite general in that they apply to repulsive multicomponent fermions, they are independent of dimensionality or trapping potential, and they hold in the ground state as well as at finite temperature.

Figure 1

Distribution of the phase for an unpolarized system of nonrelativistic repulsive fermions in one dimension at finite temperature for physical dimensionless coupling $\lambda =g\sqrt{\beta }$ of $\lambda =0.25$, 0.5, 1.0, and 2.0 (yellow, blue, green, and red, respectively); for chemical potential, $\beta \mu \simeq -0.25$, and for lattice size, $N_x^{}=41.$