High-momentum distribution with subleading $k^{-3}$ tail in the odd-wave interacting one-dimensional Fermi gases

TL;DR

This paper investigates the high-momentum distribution in one-dimensional odd-wave interacting Fermi gases, revealing a novel $k^{-3}$ tail component linked to center-of-mass motion, and establishes universal relations involving four contact parameters.

Contribution

It introduces four contact parameters necessary to fully describe the high-momentum tail up to $k^{-4}$, including a previously unknown $k^{-3}$ tail in atomic systems.

Findings

Discovery of a $k^{-3}$ tail in the momentum distribution.

Identification of four contact parameters governing high-momentum behavior.

Confirmation of results through exact two-body solutions.

Abstract

We study the odd-wave interacting identical fermions in one-dimension with finite effective range. We show that to fully describe the high-momentum distribution $\rho(k)$ up to $k^{-4}$, one needs four parameters characterizing the properties when two particles {\it contact} with each other. Two parameters are related to the variation of energy with respect to the odd-wave scattering length and the effective range, respectively, determining the $k^{-2}$ tail and part of $k^{-4}$ tail in $\rho(k)$. The other two parameters are related to the center-of-mass motion of the system, respectively determining the $k^{-3}$ tail and the other part of $k^{-4}$ tail. We point out that the unusual $k^{-3}$ tail, which has not been discovered before in atomic systems, is an intrinsic component to complete the general form of $\rho(k)$ and also realistically detectable under certain experimental conditions. Various other universal relations are also derived in terms of those contact parameters, and finally the results are confirmed through the exact solution of a two-body problem.