Wigner crystal vs. Friedel oscillations in the 1D Hubbard model

TL;DR

This paper investigates the transition between Wigner crystal and Friedel oscillations in the 1D Hubbard model, revealing a crossover influenced by finite size effects and interactions, with implications for cold atom experiments.

Contribution

It combines bosonization and DMRG to analyze density wave behavior and identifies a finite-size crossover to $4k_F$ density waves in the model.

Findings

Finite systems show a sharp crossover to $4k_F$ density waves.

Spin-incoherent fixed point can dominate behavior in finite systems.

Crossover effects are observable in cold atom experiments.

Abstract

We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with $4k_F$ density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultra cold fermionic gases in optical lattices and in finite quantum wires.