Boundary Effects on Spectral Properties of Interacting Electrons in One Dimension

TL;DR

This paper analyzes how open boundaries affect the spectral properties of interacting electrons in one dimension, revealing boundary-induced changes in critical exponents and crossover behaviors relevant for experiments.

Contribution

It provides a detailed calculation of boundary effects on spectral functions in the Tomonaga-Luttinger model using bosonization, including explicit results for the Hubbard model.

Findings

Critical exponents are altered by boundaries.

Universal bulk behavior crosses over to boundary-dominated regimes.

Crossover behavior is demonstrated in the Hubbard model.

Abstract

The single electron Green's function of the one-dimensional Tomonaga-Luttinger model in the presence of open boundaries is calculated with bosonization methods. We show that the critical exponents of the local spectral density and of the momentum distribution change in the presence of a boundary. The well understood universal bulk behavior always crosses over to a boundary dominated regime for small energies or small momenta. We show this crossover explicitly for the large-U Hubbard model in the low-temperature limit. Consequences for photoemission experiments are discussed.