Dynamical Structure Factors of the Spin-1/2 XXZ Chain with Inverse-Square Exchange and Ising Anisotropy

Abstract

The dynamical properties of the S=1/2 antiferromagnetic XXZ chain are studied by the exact diagonalization and the recursion method of finite systems up to 24 sites. Two types of the exchange interaction are considered: one is the nearest-neighbor type, and the other is the inverse-square one. As the Ising anisotropy becomes larger, there appears a noticeable difference in the transverse component S^{xx}(q,ω) between the two types of the exchange. For the nearest-neighbor type, the peak frequency of S^{xx}(q,ω) for each q approaches the center of the continuum spectrum. On the contrary, the peak frequency for the inverse-square type moves to the upper edge of the continuum, and separates from the continuum for the anisotropy larger than the threshold value. Whether the interaction between domain walls (solitons) is absent or repulsive in the Ising limit leads to this difference in the behavior of S^{xx}(q,ω). In the longitudinal component S^{zz}(q,ω), on the other hand, the feature of the dynamics is scarcely different between the two types. The energy gap and the static properties are also discussed.