Multispinon excitations in the spin S=1/2 antiferromagnetic Heisenberg model

TL;DR

This paper develops a hierarchical equations of motion approach to study multispinon excitations in the spin-1/2 antiferromagnetic Heisenberg model across different lattice geometries, aligning with experimental and numerical results.

Contribution

It introduces a novel set of equations of motion for spin susceptibilities that are independent of long-range order, providing a unified framework for analyzing low-lying excitations in various lattices.

Findings

For a chain, the boundaries match Bethe ansatz results.

In square lattices, magnons are near the lower boundary, multispinon excitations near the upper boundary.

Results are consistent with neutron scattering and numerical simulations.

Abstract

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 S=1/2 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.