Structural Evolution of 1D Spectral Function from Low- to High-Energy Limits

TL;DR

This paper provides an exact analysis of the one-electron spectral function in a 1D metal, revealing the evolution from spin-charge separation near the Fermi point to electron-like excitations at high momentum, highlighting the non-Fermi liquid behavior.

Contribution

It combines exact analysis and numerical solutions to characterize the spectral function across all momenta in a 1D metal, revealing detailed evolution of spectral features.

Findings

Near the Fermi point, spectral function shows spinon and holon peaks with a cusp.

At high momentum, the spectral function resembles a free electron but with non-quasiparticle decay.

Electron excitations exist throughout but do not conform to Fermi liquid quasiparticles.

Abstract

By exactly analyzing the spin-1/2 Luttinger liquid (LL) and numerically solving a model of a mobile impurity electron in the LL, we obtain the one-electron spectral function $A(p,\omega)$ in a one-dimensional (1D) metal in an entire range of $p$ at zero temperature. For $|p|$ near the Fermi point $p_{\rm F}$, $A(p,\omega)$ is featured by two prominent peaks of spinon and (anti)holon representing spin-charge separation, but we also find an additional cusp structure between them. For $|p| \gg p_{\rm F}$, this structure evolves as a main peak in $A(p,\omega)$ by swallowing the antiholon mode and its dispersion relation approaches the one of a free electron, implying the existence of an electron excitation in the whole region, but not quite a quasiparticle in the Fermi liquid due to ever existing power-law decay of the excitation.