The Luttinger liquid kink

TL;DR

This paper demonstrates the existence of a kink in the effective electronic dispersion of a Tomonaga-Luttinger liquid at finite temperature, which can be observed experimentally and indicates spin-charge separation.

Contribution

It reveals a measurable kink in the electronic dispersion of a Luttinger liquid, linking the low and high energy regimes to spin and charge velocities, respectively.

Findings

Existence of a kink in the dispersion at finite temperature.

The low energy dispersion follows an intermediate velocity v_l.

High energy dispersion follows the charge velocity v_c.

Abstract

Although the Tomonaga-Luttinger liquid exhibits spin-charge separation and the electron is not an elementary excitation of the system, nevertheless an effective electronic dispersion may be defined by the frequency-dependent peak in the momentum distribution curve (MDC). The MDC is defined by considering the single hole spectral function $A^<(\vec{k},\omega)$ as a function of $\vec{k}$ at a fixed frequency $\omega$. We show the existence of a \emph{kink} in this dispersion for the spin-rotationally invariant Tomonaga-Luttinger liquid at finite temperature. In the repulsive regime where the charge velocity $v_{c}$ is greater than the spin velocity $v_{s}$, the low frequency effective electronic dispersion is linear in $\vec{k}$ and follows a velocity $v_l$ between the spin and charge velocities, $v_s < v_l < v_c$. The high frequency part (which is also linear in $\vec{k}$) disperses with the charge velocity $v_c$. The energy scale of the crossover between the two velocities defines a kink, $E_{\rm kink}$. In addition, the high energy dispersion extrapolates to the Fermi energy at a wavevector $k_{ex} \ne k_F$ which is shifted from the Fermi wavevector. The presence of such a kink is measurable with, {\em e.g.}, angle-resolved photoemission experiments, and may be used to test for the presence of Luttinger liquid behavior in systems in which the separate contributions from spin and charge to the MDC are not discernible due to strong interactions or low experimental resolution.