Low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain

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 = π as well as between the ground state and the first-excited state at k = π. In the thermodynamic limit, the second-excited state at k = π 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.