Exact solutions of 1-D Hubbard model with open boundary conditions and the conformal dimensions under boundary magnetic fields

The Bethe ansatz equations of the 1-D Hubbard model under open boundaryconditions are systematically derived by diagonalizing the inhomogeneous trans-fer matrix of the XXX model with open boundaries. Through the finite-sizecorrection, we obtain the energy spectrum of the open chain and discuss the ef-fects of boundary magnetic fields applied only at the edges of the chain. Severalphysical implications of the finite-size spectrum are discussed from the view-point of the boundary conformal field theories (BCFT); the conformal dimensionof the spin excitation is quite sensitive to the boundary magnetic fields, and thissensitivity can be explained in terms of the π/2-phase shift of the BCFT. Forseveral limiting cases such as for the half-filling case, the conformal dimensionsare explicitly calculated.PACS numbers: 75.10.Hk,11.10-z,75.50.Gg, 77.80.-e e-mail: [email protected]: [email protected]