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We investigate the thermodynamic limit and exact surface energy of theisotropic spin-1 Heisenberg chain with integrable generic open boundaryconditions by a novel Bethe ansatz method. We obtain the homogeneous Betheansatz equations for the zero roots of the transfer matrix. Based on thepatterns of the zero roots, we analytical calculate the densities of zero rootsand the surface energies of the model in all regimes of the boundaryparameters.

Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries