We discuss some properties of the exact four-spinon dynamical correlation function $S_4$ in the antiferromagnetic spin 1/2 $XXX$ -model, the expression of which we derived recently. We show that the region in which it is not identically zero is different from and larger than the spin-wave continuum. We describe its behavior as a function of the neutron momentum transfer $k$ for fixed values of the neutron energy $ω$ and compare it to the one corresponding to the exact two-spinon dynamical correlation function $S_2$ . We show that the overall shapes are quite similar, even though the expression of $S_4$ is much more involved than that of $S_2$ . We finish with concluding remarks.We discuss some properties of the exact four-spinon dynamical correlation function $S_4$ in the antiferromagnetic spin 1/2 $XXX$-model, the expression of which we derived recently. We show that the region in which it is not identically zero is different from and larger than the spin-wave continuum. We describe its behavior as a function of the neutron momentum transfer $k$ for fixed values of the neutron energy $ω$ and compare it to the one corresponding to the exact two-spinon dynamical correlation function $S_2$. We show that the overall shapes are quite similar, even though the expression of $S_4$ is much more involved than that of $S_2$. We finish with concluding remarks.

arXiv:cond-mat/9802271Feb 25, 19981 citation

Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model

A. Hamid Bougourzi, M Couture, M. Kacir

We derive the exact contribution of two spinons to the dynamical correlation function of the spin-\textonehalf{} Heisenberg model. For this, we use the isotropic limits of the exact form factors that have been recently computed through the quantum affine symmetry of the anisotropic Heisenberg model $\mathrm{XXZ}$ .We derive the exact contribution of two spinons to the dynamical correlation function of the spin-\textonehalf{} Heisenberg model. For this, we use the isotropic limits of the exact form factors that have been recently computed through the quantum affine symmetry of the anisotropic Heisenberg model $\mathrm{XXZ}$.

arXiv:q-alg/9604019Physical review. B, Condensed matterNov 1, 199685 citations

Correlation Functions of Heisenberg Spin Chains

Minoru Takahashi, Masahiro Shiroishi

ButsuriMar 5, 20050 citations

Monte Carlo study of four-spinon dynamic structure function in antiferromagnetic Heisenberg model

B. Si-Lakhal, Abdessamad Abada

Using Monte Carlo integration methods, we describe the behaviour of the exact four-spinon dynamic structure function S 4 in the antiferromagnetic spin Heisenberg quantum spin chain as a function of the neutron energy ω and momentum transfer k . We also determine the four-spinon continuum, the extent of the region in the ( k , ω) plane outside which S 4 is identically zero. In each case, the behaviour of S 4 is shown to be consistent with the four-spinon continuum and compared to that of the exact two-spinon dynamic structure function S 2 . Overall shape similarity is noted.Using Monte Carlo integration methods, we describe the behaviour of the exact four-spinon dynamic structure function S 4 in the antiferromagnetic spin Heisenberg quantum spin chain as a function of the neutron energy ω and momentum transfer k . We also determine the four-spinon continuum, the extent of the region in the ( k , ω) plane outside which S 4 is identically zero. In each case, the behaviour of S 4 is shown to be consistent with the four-spinon continuum and compared to that of the exact two-spinon dynamic structure function S 2 . Overall shape similarity is noted.

Journal of Physics A Mathematical and GeneralDec 15, 20034 citations

We discuss some properties of the exact four-spinon dynamical correlation function

S_4

in the antiferromagnetic spin 1/2

XXX

-model, the expression of which we derived recently. We show that the region in which it is not identically zero is different from and larger than the spin-wave continuum. We describe its behavior as a function of the neutron momentum transfer

k

for fixed values of the neutron energy

ω

and compare it to the one corresponding to the exact two-spinon dynamical correlation function

S_2

. We show that the overall shapes are quite similar, even though the expression of

S_4

is much more involved than that of

S_2

. We finish with concluding remarks.

\mathrm{XXZ}