Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

TL;DR

This paper constructs the spectral function of the Luther-Emery model for one-dimensional fermions, revealing how spectral features vary with different gaps and velocities, and discusses implications for photoemission experiments.

Contribution

It provides a detailed analytical construction of spectral functions for the Luther-Emery model, connecting symmetries and known limits, and extends to multi-particle correlations.

Findings

Spectral functions differ based on charge/spin gaps and velocities.

Peierls systems show one singularity with anomalous dimension.

Superconductors exhibit two singularities with anomalous dimensions.

Abstract

I construct the spectral function of the Luther-Emery model which describes one-dimensional fermions with one gapless and one gapped degree of freedom, i.e. superconductors and Peierls and Mott insulators, by using symmetries, relations to other models, and known limits. Depending on the relative magnitudes of the charge and spin velocities, and on whether a charge or a spin gap is present, I find spectral functions differing in the number of singularities and presence or absence of anomalous dimensions of fermion operators. I find, for a Peierls system, one singularity with anomalous dimension and one finite maximum; for a superconductor two singularities with anomalous dimensions; and for a Mott insulator one or two singularities without anomalous dimension. In addition, there are strong shadow bands. I generalize the construction to arbitrary dynamical multi-particle correlation functions. The main aspects of this work are in agreement with numerical and Bethe Ansatz calculations by others. I also discuss the application to photoemission experiments on 1D Mott insulators and on the normal state of 1D Peierls systems, and propose the Luther-Emery model as the generic description of 1D charge density wave systems with important electronic correlations.