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 onlyone of the boundary sites has a different value of chemical potential.We consider the case when the boundary site has a negative chemicalpotential −p and the Hubbard coupling U is positive. By an analyticmethod we show that when p is larger than the transfer integral someof the ground-state solutions of the Bethe ansatz equations becomecomplex-valued. It follows that there is a “surface phase transition”at some critical value pc; when p < pc all the charge excitations havethe gap for the half-filled band, while there exists a massless chargemode when p >pc. Institute for Theoretical Physics, State University of New York, Stony Brook, NY11794-3840, USA, [email protected]; On leave from Ochanomizu Univer-sity, [email protected] .Address after June 1998: Institute of Modern Physics, Northwest University, Xian710069, China, [email protected] .