Fermi-edge singularity in a spin-incoherent Luttinger liquid

TL;DR

This paper theoretically analyzes the Fermi edge singularity in a spin-incoherent Luttinger liquid, revealing how the absorption edge behavior depends on core hole mass, interaction parameters, and magnetic field, with distinct results from the spin coherent case.

Contribution

It introduces a theoretical framework for the Fermi edge singularity in spin-incoherent Luttinger liquids, highlighting differences from the spin coherent case and mapping to spinless models in the infinite mass limit.

Findings

Absorption edge behaves as $( ext{frequency}- ext{threshold})^ ext{exponent}/ ext{logarithmic factor}$ for finite core hole mass.

Exponent depends on interaction parameter $g$ and electron-hole coupling, but not on magnetic field or core hole mass.

In the infinite mass limit, the problem maps onto a spinless Luttinger liquid with a universal exponent contribution.

Abstract

We theoretically investigate the Fermi edge singularity in a spin incoherent Luttinger liquid. Both cases of finite and infinite core hole mass are explored, as well as the effect of a static external magnetic field of arbitrary strength. For a finite mass core hole the absorption edge behaves as $(\omega-\omega_{\rm th})^\alpha/ \sqrt{|\ln(\omega-\omega_{\rm th})|}$ for frequencies $\omega$ just above the threshold frequency $\omega_{\rm th}$. The exponent $\alpha$ depends on the interaction parameter $g$ of the interacting one dimensional system, the electron-hole coupling, and is independent of the magnetic field strength, the momentum, and the mass of the excited core hole (in contrast to the spin coherent case). In the infinite mass limit, the spin incoherent problem can be mapped onto an equivalent problem in a spinless Luttinger liquid for which the logarithmic factor is absent, and backscattering from the core hole leads to a universal contribution to the exponent $\alpha$.