Infrared catastrophe and tunneling into strongly correlated electron systems: Perturbative x-ray edge limit

TL;DR

This paper investigates spectral anomalies in strongly correlated electron systems caused by an infrared catastrophe during tunneling, introducing a nonperturbative method based on x-ray edge physics applicable across various models.

Contribution

It develops a nonperturbative functional-integral approach to explain tunneling anomalies, extending x-ray edge methods to strongly correlated electron systems of any dimensionality.

Findings

Qualitative agreement with known spectral features in 1D and 2D systems

Applicable to lattice and continuum models with or without translational invariance

Provides a unified framework for understanding tunneling anomalies

Abstract

The tunneling density of states exhibits anomalies (cusps, algebraic suppressions, and pseudogaps) at the Fermi energy in a wide variety of low-dimensional and strongly correlated electron systems. We argue that in many cases these spectral anomalies are caused by an infrared catastrophe in the screening response to the sudden introduction of a new electron into the system during a tunneling event. A nonperturbative functional-integral method is introduced to account for this effect, making use of methods developed for the x-ray edge singularity problem. The formalism is applicable to lattice or continuum models of any dimensionality, with or without translational invariance. An approximate version of the technique is applied to the 1D electron gas and the 2D Hall fluid, yielding qualitatively correct results.