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

TL;DR

This paper extends path-integral methods from lattice QCD to nonrelativistic repulsive Fermi gases, revealing how Tan's contact encapsulates complex phase cancellations, with broad applicability across various fermionic systems.

Contribution

It generalizes complex-phase analysis techniques from QCD to nonrelativistic Fermi gases, linking Tan's contact to phase cancellations and validating assumptions with Monte Carlo and perturbative methods.

Findings

Tan's contact involves nontrivial cancellations of phase-dependent terms.

Gaussian phase distribution is supported by Monte Carlo and perturbative results.

Results apply broadly to multi-component, polarized, and fixed-particle-number systems.

Abstract

Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to non-relativistic 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 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 multi-component fermions, are independent of dimensionality or trapping potential, and hold in the ground state as well as at finite temperature.