With the commutation relations of the spin operators, we first write out the equations of motion of the spin susceptibility and related correlation functions that have a hierarchical structure, then under the “soft cut-off” approximation, we give a set of equations of motion of spin susceptibilities for a spin [Formula: see text] antiferromagnetic Heisenberg model that is independent of whether or not the system has a long-range order in the low energy/temperature limit. Applying for a chain, a square lattice and a honeycomb lattice, respectively, we obtain the upper and the lowest boundaries of the low-lying excitations by solving this set of equations. For a chain, the upper and the lowest boundaries of the low-lying excitations are the same as that of the exact ones obtained by the Bethe ansatz, where the elementary excitations are the spinon pairs. For a square lattice, the spin wave excitation (magnons) resides in the region close to the lowest boundary of the low-lying excitations, and the multispinon excitations take place in the high-energy region close to the upper boundary of the low-lying excitations. For a honeycomb lattice, we have one kind of “mode” of the low-lying excitation. The present results obey the Lieb–Schultz–Mattis theorem, and they are also consistent with recent neutron scattering observations and numerical simulations for a square lattice.
Multispinon excitations in the spin S = 1/2 antiferromagnetic Heisenberg model
