Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice

Abstract

Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu\(_3\)(OH)\(_6\)C\(_{12}\) (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions. In contrast to existing theoretical models of spin liquids, the measured dynamic structure factor reveals an excitation continuum which is remarkably at as a function of frequency and has almost no momentum dependence along several high-symmetry directions. Here we show that many experimentally observed features can be explained by the presence of topological vison excitations in a Z\(_2\) spin liquid. These visons form at bands on the kagome lattice, and thus act as a momentum sink for spin-carrying excitations which are probed by neutron scattering. We compute the dynamic structure factor for two di fferent Z\(_2\) spin liquids and find that one of them describes Herbertsmithite well above a very low energy cutoff.