Theory of hole propagation in one dimensional insulators and superconductors

TL;DR

This paper develops a theoretical framework for understanding hole propagation in one-dimensional insulators and superconductors, revealing complex spectral features and connections to impurity problems in Luttinger liquids.

Contribution

It introduces a comprehensive analysis of hole dynamics using bosonization, perturbation theory, and Bethe ansatz, highlighting effects of magnetic fields and spin anisotropy.

Findings

Spectral functions exhibit rich structures with broken spin isotropy.

Connections established between hole propagation and impurity problems in Luttinger liquids.

Predictions of exotic momentum dependence in photoemission spectra.

Abstract

The dynamical properties of hole motion in an antiferromagnetic background are determined in one dimensional models in zero magnetic field, where spin isotropy holds, as well as in an external magnetic field. The latter case is also relevant, via particle-hole transformation, to the problem of hole propagation in one dimensional "superconductors". The singularities in the spectral function are investigated by means of bosonization techniques and perturbation theories. Results are then compared with Bethe ansatz solutions and Lanczos diagonalizations. The formalism also leads to interesting connections to the single impurity problem in Luttinger liquids. A rich structure is found in the spectral function whenever spin isotropy is broken, suggesting the presence of exotic momentum dependence in photoemission spectra of (quasi) one dimensional materials.