TABLE OF CONTENTS In this chapter we shall present the results of the Bethe ansatz studies for quantum spin and correlated electron chains with open boundary conditions and shall discuss the effects of local potentials or fields applied to open edges of quantum chains. The important generalization of the algebraic Bethe ansatz for open chains will also be presented here.
So far we considered spin and correlated electron chains with periodic boundary conditions, i.e., we considered chains in the ring geometry. However, the reader can ask the question: what will happen if a chain is not closed in a ring?
At the level of the Hamiltonian it means that we have to equate the terms like S x,y,z L S x,y,z 1, a L ? a 1 ?, a 1 ? a L ? and n L ? n 1 ? to zero in previous formulae. To have more general results, we can add some boundary magnetic fields to the Hamiltonian of a spin chain with open boundary conditions as
For the case of a correlated electron chain we can add not only the term Eq. (6.1), but also the term
which determines the action of boundary potentials (for example, related to point contact potentials applied only to edges of a chain). We shall call the case with h 1 = h L = ? 1 = ? L = 0 the situation...
