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

TL;DR

This paper introduces a nonperturbative method to calculate electron propagators in strongly correlated systems, extending the x-ray edge approach by including fluctuations, and accurately predicts the density of states in one-dimensional models.

Contribution

It develops a cumulant expansion technique to incorporate fluctuations beyond the x-ray edge limit for strongly correlated electron systems.

Findings

Accurately predicts power-law density of states in 1D systems.

Recovers exact DOS for the Tomonaga-Luttinger model.

Provides a general framework applicable to various models and dimensions.

Abstract

We develop a nonperturbative method to calculate the electron propagator in low-dimensional and strongly correlated electron systems. The method builds on our earlier work using a Hubbard-Stratonovich transformation to map the tunneling problem to the x-ray edge problem, which accounts for the infrared catastrophe caused by the sudden introduction of a new electron into a conductor during a tunneling event. Here we use a cumulant expansion to include fluctuations about this x-ray edge limit. We find that the dominant effect of electron-electron interaction at low energies is to correct the noninteracting Green's function by a factor exp(-S), where S can be interpreted as the Euclidean action for a density field describing the time-dependent charge distribution of the newly added electron. Initially localized, this charge distribution spreads in time as the electron is accommodated by the host conductor, and during this relaxation process action is accumulated according to classical electrostatics with a screened interaction. The theory applies to lattice or continuum models of any dimensionality, with or without translational invariance. In one dimension the method correctly predicts a power-law density of states (DOS) for electrons with short-range interaction and no disorder, and when applied to the solvable Tomonaga-Luttinger model, the exact DOS is obtained.