Non-Linear Excitations in Haldane Spin Chains

Jack A. Tuszyński, J.M. Dixon

Claudette E. Cordeiro

L. P. Régnault, Igor A. Zaliznyak, S. V. Meshkov

The low-temperature behaviour of the thermodynamic quantities in the one-dimensional 1D antiferromagnet with a Haldane ground state was analysed using a concept of non-interacting quasiparticles as a starting point. The proposed description appeared to be in good agreement with the results of the Monte Carlo study of a 128-site spin chain and experimental data obtained in NENP (Ni(C 2 H 8 N 2 ) 2 NO 2 ClO 4 ) provided that the elementary excitations constituting the Haldane triplet obey Fermi statistics.

Antonio S. T. Pires, M. E. Gouvêa

RRcent theoretical and experimental results on non-linear excitations in one dimensional classical antiferromagnetic chains are reviewed with a particular emphasis on dynamic properties. The main investigated substance is TMMC which can be regarded as a quasi-onedimensional antiferromagnet with easy plane anisotropy. A discussion of Haldane's conjecture that there is an excitation gap for integer, but not half-integer spin is given. The open questions and possible investigation for the future are discussed.

C. Broholm

Yue Yu, Qian Niu

We formulate the dynamics of local order parameters by extending the recently developed adiabatic spinwave theory involving the Berry curvature, and derive a formula showing explicitly the role of the Berry phase in determining the spectral form of the low-lying collective modes. For antiferromagnetic spin chains, the Berry phase becomes a topological invariant known as the Chern number. Our theory predicts the existence of the Haldane gap for a topologically trivial ground state, and a linear dispersion of low-lying excitations for a non-trivial ground state.