Numerical Calculations of S=1 Heisenberg Antiferromagnetic Chain

KIYOMI OKAMOTO

Jizhong Lou, Shaojin Qin, Zhao-Bin Su

Using the density-matrix renormalization-group (DMRG) technique, we carry out a large scale numerical calculation for the $S=2$ antiferromagnetic Heisenberg (AFH) chain. We obtain the magnetization curve of $S=2$ chain near the critical field. The corrections to the magnetization due to the magnon-magnon interaction are the same order for $S=2$ and $S=1$ chains. By comparing the experimental magnetization with our calculation, we find that the gap obtained experimentally is about $0.08J$ which is close to the accurate DMRG estimation for the $S=2$ AFH chain. Numerical errors in our large scale calculation are also discussed.

Julia Mihailowa Wesselinowa

The one-dimensional spin-1 Heisenberg antiferromagnetic chain is studied by a Green's function technique. The excitation spectrum is obtained. The dispersion of excitations for an infinite isotropic chain is numerically calculated. At k = 0 we obtain a gap 2Δ which is equal to 0.826J and at k = π we obtain Δ = 0.41J, which is in very good agreement with the exact numerical results of White and Huse.

Tôru Sakai

Yoshihiro Nishiyama, Keisuke Totsuka, Naomichi Hatano +1 more

Kazuo Hida

The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum k by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small k, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.