Singular responses of spin-incoherent Luttinger liquids

TL;DR

This paper reviews the unique singular response behaviors of spin-incoherent Luttinger liquids, highlighting their universal features, deviations from traditional models, and discussing experimental and theoretical challenges.

Contribution

It provides a comprehensive review of the singular responses in spin-incoherent Luttinger liquids, emphasizing their universal characteristics and differences from conventional models.

Findings

Singular responses often include logarithmic corrections.

Responses exhibit higher universality independent of microscopic details.

The paper summarizes experimental status and theoretical challenges.

Abstract

When a local potential changes abruptly in time, an electron gas shifts to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is relevant for the so-called X-ray edge or Fermi edge singularity, and for tunneling into an interacting one dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: $(\frac{\omega_{\rm th}}{\omega-\omega_{\rm th}})^\alpha\Theta(\omega-\omega_{\rm th})$ where $\omega_{\rm th}$ is a threshold frequency and $\alpha$ is an exponent characterizing the singular response. In this paper singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized, and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted.