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We investigate the thermodynamic limit of the one-dimensional ferromagneticXXZ model with twisted (or antiperiodic ) boundary condition. It is shown thatthe distribution of the Bethe roots of the inhomogeneous Bethe Ansatz equations(BAEs) for the ground state as well as for the low-lying excited states satisfythe string hypothesis, although the inhomogeneous BAEs are not in the standardproduct form which has made the study of the corresponding thermodynamic limitnontrivial. We also obtain the twisted boundary energy induced by thenon-trivial twisted boundary conditions in the thermodynamic limit.

Twisted boundary energy and low energy excitation of the XXZ spin torus at the ferromagnetic region