Splitting of Fermi point of strongly interacting electrons in one dimension: A nonlinear effect of spin-charge separation

TL;DR

This paper demonstrates that in strongly interacting one-dimensional electrons, spin-charge separation can cause the Fermi point to split into two, with a second singularity at 3k_F formed solely by charge modes, extending the known low-energy effects.

Contribution

It reveals a nonlinear effect of spin-charge separation in strongly coupled 1D electrons, showing the Fermi point splitting beyond low-energy Luttinger liquid theory.

Findings

Identification of an additional singularity at 3k_F in momentum distribution

The second singularity is of the same Luttinger liquid type as at k_F

The second Luttinger liquid involves only charge modes, not spin

Abstract

A system of one-dimensional electrons interacting via a short-range potential described by Hubbard model is considered in the regime of strong coupling using the Bethe ansatz approach. We study its momentum distribution function at zero temperature and find one additional singularity, at the $3k_{\mathrm{F}}$ point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at $k_{\mathrm{F}}$. By calculating the spectral function simultaneously, we show that the second Luttinger liquid at $3k_{\mathrm{F}}$ is formed by charge modes only, unlike the known one around $k_{\mathrm{F}}$ consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.