Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

TL;DR

This paper investigates how a dynamic quantum impurity influences spatial electron correlations in a one-dimensional electron gas, revealing slow decay and power-law energy dependence characteristic of the Fermi edge singularity.

Contribution

It provides compact formulas for correlation functions showing the impurity's impact on spatial correlations and their decay behavior.

Findings

Correlations decay as the third inverse power of distance.

Spatial correlations exhibit power-law energy dependence.

Impurity induces long-range correlations with slow decay.

Abstract

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a non-trivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.