The four-spinon dynamical structure factor of the Heisenberg chain

Abstract

We compute the exact 4-spinon contribution to the zero-temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit. We make use of the expressions for matrix elements of local spin operators obtained by Jimbo and Miwa using the quantum affine symmetry of the model, and of their adaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall factors). The 4-spinon contribution to the first frequency moment sum rule at fixed momentum is calculated. This shows, as expected, that most of the remaining correlation weight above the known 2-spinon part is carried by 4spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.

Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds

“…We analyse our data by fitting the Q chain -dependent intensity of 1D constant-energy cuts at different energy transfers to the exact dynamical structure factor for the 1D spin-1/2 Heisenberg Hamiltonian including both the two-spinon and four-spinon contributions to S(Q chain , E) (ref. 25). Although higher-order excitations will also form a part of the excitation continuum, the calculated spectral weight arising from these two contributions is about 98% of the total, which is within our experimental error.…”

“…The data cover two 1D Brillouin zones and were not symmetrized. Magnetic scattering corresponding to the multispinon triplet continuum 25 emanating from Q chain = ±0.5, where it is most intense, and extending to E ∼ 600 meV, is clearly seen repeated in both Brillouin zones. The continuum of excitations filling large regions of (Q chain ,E) phase space is clearly visible in Fig.…”

“…The situation is very different in 1D, where recent progress in the theory of integrable models has led to the development of an extremely accurate quantitative theory for the dynamical spin correlations 25 . Here, we report a detailed INS measurement of magnetic excitations in the 1D prototype cuprate material Sr 2 CuO 3 , the crystal structure of which is shown in Fig.…”

“…25) and using the anisotropic magnetic form factor of the Cu 2+ ion, following the procedure adopted in previous studies 6,13,28,29 . Only two parameters are varied in such fitting: the in-chain exchange coupling J , which determines the overall energy scale of magnetic excitations, and the prefactor A, which accounts for the possible statistical and systematic errors of our intensity measurements and ideally should be equal to one.…”

The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain

“…In future publications, we will consider the longitudinal structure factor S zz (k, ω) in the same regime, as well as the four-spinon contribution to the transverse structure factor, thereby generalizing the recent results of the isotropic case [23] to this sector. An interesting further line of investigation would be to apply the algebraic approach within the gapless anisotropic regime.…”