Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields

1 The thermodynamic limit and boundary energy of the isotropic spin-1 Heisen2 berg chain with non-diagonal boundary fields are studied. The finite size scal3 ing properties of the inhomogeneous term in the T −Q relation at the ground 4 state are analyzed. Based on the reduced Bethe ansatz equations (BAEs), we 5 obtain the boundary energy of the system. These results can be generalized 6 to the SU(2) symmetric high spin Heisenberg model directly. 7