A GAPLESS CHARGE MODE INDUCED BY THE BOUNDARY STATES IN THE HALF-FILLED HUBBARD OPEN-CHAIN

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 o f the boundary sites has a different value of chemical potential. We c onsider the case when the boundary site has a negative chemical potent ial - 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 g round-state solutions of the Bethe ansatz equations become complex-val ued. It follows that there is a 'surface phase transition' at some cri tical value p(c); when p < p(c) all the charge excitations have the ga p for the half-filled band, while there exists a massless charge mode when p > p(c).