Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid

TL;DR

This paper provides exact solutions to the x-ray edge problem for 1D and 2D strongly correlated electron systems, clarifying the effects of recoil corrections on the tunneling density of states and confirming qualitative predictions.

Contribution

It offers the first exact solutions of the Nozieres-De Dominicis equations for these models, refining understanding of infrared catastrophe effects in low-dimensional electron systems.

Findings

Exact solution modifies the DOS exponent in 1D electron gas.

No change in the DOS for 2D Hall fluid with short-range interactions.

First exact solution for the 2D electron gas in the lowest Landau level.

Abstract

In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the 1D electron gas and 2D Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozieres-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the 1D case but finding no changes in the DOS of the 2D Hall fluid with short-range interaction. We also provide, for the first time, an exact solution of the Nozieres-De Dominicis equation for the 2D electron gas in the lowest Landau level.