Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions

Abstract

We study, by means of exact-diagonalization techniques, the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays, at strong coupling, very well pronounced Wigner oscillations with a 4k F periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.

Three interacting atoms in a one-dimensional trap: a benchmark system for computational approaches

“…CI predictions nicely match VM results for repulsive interactions, the smaller g the better the agreement. This converging behavior is generic to long-range repulsive interactions in one [36,52,53,59,60,62,64,65] and two dimensions [46,47,[81][82][83][84]. However, the performance of the CI method is poor on the attractive side, with Figure 9.…”

“…Together with quantum Monte Carlo [9,[48][49][50][51], CI provides the ground-state energy within principle-arbitrary accuracy, hence it has been widely applied to one-dimensional systems of finite size [28,30,31,33,36,39,46,[52][53][54][55][56][57][58][59][60][61][62][63][64][65]. However, for strong attractive interactions, the two-body wave function tends to collapse in space [44], hence the convergence of the calculation should be carefully assessed.…”

“…This has fueled theoretical proposals that are specific to few-atom traps, focusing on themes as diverse as Stoner ferromagnetism [27][28][29][30][31][32], exchange mechanisms [33,34], Wigner localization [35,36], quasiparticle- [37] and pair-tunneling [38], the FuldeFerrell-Larkin-Ovchinnikov state [39], pairing [40], mesoscopic phase separations for bosons [41]. On one hand, the study of few interacting atoms, which are the bulding blocks of many-body states, gives an insight into the essential physical features of more complex quantum systems.…”

2kF-Friedel to4kF-Wigner oscillations in one-dimensional Fermi gases under confinement

“…However, in one dimension, the equilibrium positions of the electrons are assumed to be equally spaced, and a solid-like state can be produced when the correlation length exceeds the sample length [4]. The liquid-to-quasi-Wigner crystal crossover when the density decreases can be characterized by the onset of the 4k F peak in the static structure factor following from the Luttinger liquid predictions [2,5], with k F being the Fermi wave vector (related to the fermion density n by k F = πn/2), or by the N f − 1 high-contrast peaks in the pair-correlation function [6], with N f being the particle number of the system.…”

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

“…As the density distribution is not solely a convincing criteria of Wigner crystal, the density-density correlation function plays an important role in characterizing the Wigner crystal phase [31]. In the present work, we shall study both the density distribution and density correlation function of the Hubbard model either without or with long-range interactions.…”