A gapless charge mode induced by the boundary states in the half-filled Hubbard open-chain

TL;DR

This paper demonstrates that boundary states in a half-filled Hubbard chain can induce a gapless charge mode, revealing a surface phase transition driven by boundary chemical potential.

Contribution

It analytically shows the emergence of a gapless charge mode induced by boundary states in the Hubbard model with boundary chemical potential.

Findings

Charge gap exists for p < p_c

Massless charge mode appears for p > p_c

Surface phase transition at critical p_c

Abstract

We discuss the ground state and some excited states of the half-filled Hubbard model defined on an open chain with L sites, where only one of the boundary sites has a different value of chemical potential. We consider the case when the boundary site has a negative chemical potential -p and the Hubbard coupling U is positive. By an analytic method we show that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. It follows that there is a ``surface phase transition'' at some critical value p_c; when p<p_c all the charge excitations have the gap for the half-filled band, while there exists a massless charge mode when p>p_c.