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.

• Received 3 January 2022
• Revised 21 February 2022
• Accepted 1 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.L121112