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

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.

6 pages, 1 figure

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Cited by in corpus (9)

• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Measures of complexity and entanglement in fermionic many-body systems
• On the Statistics of Baryon Correlation Functions in Lattice QCD
• Entanglement entropy, single-particle occupation probabilities, and short-range correlations
• Path integral contour deformations for noisy observables
• Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion
• Phase Unwrapping and One-Dimensional Sign Problems
• Large-time correlation functions in bosonic lattice field theories
• Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem