  In order to confirm the picture of domain-wall excitations in the hidden
antiferromagnetic order of the Haldane phase, the structure of the low-lying
excitations in the S=1 antiferromagnetic Heisenberg chain is studied by a
quantum Monte Carlo method. It is confirmed that there exists a finite energy
gap between the first- and the second-excited states at $k=\pi$ as well as
between the ground state and the first-excited state at $k=\pi$. In the
thermodynamic limit, the second-excited state at $k=\pi$ is separated from the
ground state by the gap which is three times as large as the Haldane gap. From
the size dependences of the low-lying-excitation energies, the interactions
between the elementary excitations in the excited states are concluded to be
repulsive.
