Threshold Singularities in the One Dimensional Hubbard Model

TL;DR

This paper analyzes threshold singularities in the single-particle Green's function of the 1D Hubbard model below half-filling, using finite-size corrections and extending results to the Yang-Gaudin model with delta interactions.

Contribution

It provides a detailed calculation of finite-size corrections and threshold singularities, extending the analysis to the Yang-Gaudin model with delta-function interactions.

Findings

Finite-size corrections to energy calculated for hole excitations.

Threshold singularities in Green's function determined.

Results applicable to both Hubbard and Yang-Gaudin models.

Abstract

We consider excitations with the quantum numbers of a hole in the one dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model (electron gas with delta-function interactions).