Dynamical properties of one-dimensional quantum systems

Abstract

The dynamical structure factors of XXZ chain with anisotropy were studied by the exact diagonalization and the recursion method of finite systems, focusing on changes of the dynamical feature in introducing Ising anisotropy. Both of the longitudinal component S(sup zz)(q,omega) and the traversal component S(sup xx)(q,omega) were calculated in following two types of exchange interactions. One was the nearest-neighbor type and the other was inverse-square-distance type. The intensity of the longitudinal component at omega asymptotic to zero and q equals to pi became to be conspicuously enhanced with increasing Ising anisotropy in both types of the exchange interactions. The peak position of the traversal component were approached the center of the continuum spectrum in the nearest-neighbor type as Ising anisotropy became larger. On the contrary, it moved to the upper edge of continuum in the inverse-square-distance type. Thus, the nature of the degeneracy of the first exited states is different between two types.

異方性を持つXXZ鎖の力学的構造因子を、完全対角化法と有限系の再帰法を用いて、イジング異方性の誘導における力学的特徴の変化に注目して研究した。2種の交換相互作用、最隣接型と逆2乗距離型において、縦成分S(sup zz)(q,ω)と横成分S(sup xx)(q,ω)の両方を計算した。両方の交換相互作用において、ωが0にほぼ等しくq=πで、縦成分の強度は、イジング異方性の増加にともなって著しく増加するようになった。横成分のピークの位置は、最隣接型においては、イジング異方性が大きくなるとともに連続スペクトルの中央に近づいていく。対して、逆2乗距離型では、連続値の上端に移動していく。このように、1次励起状態の縮退の性質は2種の交換相互作用において異なる。