Dynamical properties and elementary excitations of one-dimensional quantum systems

Abstract

The static and dynamical properties for the spin-1/2 XXZ chain with inverse-square exchange and Ising anisotropy have numerically been investigated. The dynamic structure factor of the XXZ chain has been studied in order to clarify the effects of the Ising anisotropy and the interaction range on dynamics. It was indicated that there are two types of the exchange interactions, that is, nearest-neighbor type and the inverse square type. The study has been focused on the characteristic change when the Ising anisotropy was increased. There appeared a noticeable difference between the two types of the exchange in the transverse component. This difference was understood in terms of whether the interaction between domain wall is absent or repulsive in the Ising limit. The energy gap in the magnetic excitation has been evaluated using the results of the transverse component. It was found for the inverse-square type that the opening of the gap was even slower than that for the nearest-neighbor type.

逆2乗交換とイジング異方性を有するスピン-1/2-XXZ鎖に対する静的および動的特性を数値的に検討した。イジング異方性と動力学上の相互作用範囲の影響を明らかにするためXXZ鎖の動的構造因子を研究した。最隣接型と逆2乗型の2種の交換相互作用があることを指摘した。イジング異方性が増加した場合の特性変化に焦点を当てて研究した。横成分に関して、2種の交換の間に顕著な違いが出現した。この差異は磁壁間の相互作用が欠けているか、あるいはイジング限界で反発するか否かによると理解した。磁気励起の際のエネルギーギャップを、横成分の結果を用いて評価した。逆2乗型について、間隔最隣接型のギャップの開放に比べてかなり緩慢であることが分かった。