High-momentum oscillating tails of strongly interacting 1D gases in a box

TL;DR

This paper investigates how rigid walls influence the momentum distribution in strongly interacting 1D gases, revealing that finite-size effects and long-range correlations significantly modify the expected $1/k^4$ tail.

Contribution

It demonstrates that boundary effects alter Tan's relation in 1D gases and shows that oscillating tails encode long-range spin correlations, a novel insight.

Findings

The $1/k^4$ tail is affected by boundary-induced finite-size effects.

Oscillating tails contain information on long-range spin correlations.

Rigid walls break the standard Tan's relation in 1D systems.

Abstract

We study the momentum distribution of strongly interacting one-dimensional mixtures of particles at zero temperature in a box potential. We find that the magnitude of the $1/k^4$ tail of the momentum distribution is not only due to short-distance correlations, but also to the presence of the rigid walls, breaking the Tan's relation relating this quantity to the adiabatic derivative of the energy with respect to the inverse of the interaction strength. The additional contribution is a finite-size effect that includes a $k$-independent and an oscillating part. This latter, surprisingly, encodes information on long-range spin correlations.