Some aspects of functional Bethe ansatz

TL;DR

This paper examines the validity of the Bethe ansatz wave function in impurity problems and suggests modifications to the Hubbard model to preserve known solutions, highlighting overlooked aspects in existing methods.

Contribution

It reveals overlooked issues in solving the Hubbard model with Bethe ansatz and proposes a way to modify the Hamiltonian to maintain the validity of solutions.

Findings

Bethe ansatz wave function validity is confirmed for impurity problems

An overlooked point in Hubbard model solutions is identified

A modification to the Hamiltonian is proposed to preserve solutions

Abstract

The validity of Bethe ansatz wave function without the backward scattering for the problem of impurity in correlated hosts with periodic boundary condition is illustrated by a simple example of quantum mechanics. An long being overlooked point in solving Hubbard model by means of Bethe ansatz is indicated. A possible repairing on the Hamiltonian is suggested so that the well known solution is still valid.