2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement

TL;DR

This paper investigates the transition from Friedel to Wigner oscillations in one-dimensional Fermi gases with contact interactions, using density-functional theory and exact methods, revealing a crossover characterized by density profile peaks.

Contribution

It demonstrates the crossover from Friedel to Wigner oscillations in 1D Fermi gases and identifies the interaction strength threshold for Wigner oscillations using Bethe-ansatz-based DFT and exact solutions.

Findings

Number of peaks doubles in unpolarized systems indicating crossover

Wigner oscillations with 4k_F wave vector appear at a threshold interaction strength

Density profiles show clear signatures of the oscillation transition

Abstract

Density oscillations of confined one-dimensional Fermi gases of contact repulsive interactions in a continuous space are discussed within Bethe-ansatz-based spin-density-functional theory. The results are compared against the exact analytical and the exact diagonalization method. For an unpolarized system, the number of peaks in the density profiles is doubled, signaling the crossover of the 2k_F-Friedel to 4k_F-Wigner oscillations (with kF being the Fermi wave vector). For both unpolarized and polarized systems, a threshold of the short-range interaction strength can be found where Nf-peak Wigner oscillations of a 4k_F wave vector appear in the density profile (N_f is the total particle number).