Instability of the Mott or Lieb-Wu insulator caused by an infinitesimal perturbation

TL;DR

This paper demonstrates that the half-filled ground state of the one-dimensional Hubbard model is inherently unstable to infinitesimal perturbations due to the Kondo effect, challenging the traditional view of it as a Mott insulator.

Contribution

It reveals that the insulating ground state in the 1D Hubbard model is unstable under infinitesimal perturbations, questioning the established Mott insulator classification.

Findings

Any insulating ground state with a full gap is unstable with infinitesimal perturbation.

The Kondo effect causes the instability of the Mott insulator in 1D.

The rigorous Bethe-ansatz result is a necessary but not sufficient condition for insulating ground state.

Abstract

The half-filled ground state of the Hubbard model in one dimension is studied by Kondo-lattice theory. Because of the Kondo effect, any insulating ground state with a complete gap open is unstable in the presence of an infinitesimal perturbation. This fact casts doubt on the claim by E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968) that the half-filled ground state is the Mott insulator. Though the claim is based on a rigorous result given by the Bethe-ansatz solution, the rigorous result is simply a necessary condition for the ground state being an insulator.