Spectrum of boundary states in the open Hubbard chain

TL;DR

This paper investigates the boundary-bound states in the open Hubbard chain using Bethe Ansatz, revealing how boundary potentials influence the ground state and boundary excitations, with implications for boundary conformal field theory.

Contribution

It provides a detailed analysis of boundary states in the open Hubbard model, including finite size corrections and boundary conformal field theory predictions, which are novel in this context.

Findings

Boundary potentials determine the boundary state composition.

Bound states include single charge, electron pairs, holon, and spinon states.

Finite size corrections align with boundary conformal field theory predictions.

Abstract

We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one finds that the true ground state contains a single charge or, for boundary potentials comparable to the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.