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

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.

18 pages, 5 figures

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• Spin-charge separation and localization in one-dimension
• Probing spin-charge separation in a Tomonaga-Luttinger liquid
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Energy relaxation and thermalization of hot electrons in quantum wires
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• Collective modes in the charge-density wave state of K${}_{0.3}$MoO${}_3$: The role of long-range Coulomb interactions revisited
• Dominant end-tunneling effect in two distinct Luttinger liquids coexisting in one quantum wire