Physical picture of the gapped excitation spectrum of the one-dimensional Hubbard model

TL;DR

This paper introduces an intuitive Bethe-Ansatz-based classification for the spectrum of the 1D Hubbard model, proving a string hypothesis and deriving exact equations, revealing that all gapped states share the same Bethe-Ansatz form.

Contribution

It provides a new, simple physical picture for the gapped excitation spectrum and proves a string hypothesis for complex momenta in the 1D Hubbard model.

Findings

All gapped eigenstates have Bethe-Ansatz form.

Derived exact Bethe-Ansatz equations including all states.

Computed dispersion of excitations near half-filling.

Abstract

A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-Ansatz approach. This approach allows us to prove a "string hypothesis" for complex momenta and derive an exact formulation of the Bethe-Ansatz equations including all states. Among other things we show that all gapped eigenstates have the Bethe-Ansatz form, contrary to assertions in the literature. The simplest excitations in the upper Hubbard band are computed: we find an unusual dispersion close to half-filling.