Dynamical Structure Factors of the Spin-1/2XXZChain 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.KEYWORDS: dynamical structure factor, XXZ chain, inverse-square exchange, nearest-neighbor exchange, Ising anisotropy, Haldane-Shastry model, exact diagonalization, recursion method §1. IntroductionThe physics concerning one-dimensional (1D) quantum systems has been a long-standing problem. Discovery of many quasi-1D quantum magnets has spurred on the studies of the systems. Among those, there are S = 1/2 systems in which a finite energy gap opens in the magnetic excitation spectrum. These systems have various origins of an excitation gap. For example, in CuGeO 3 , the first inorganic compound in which a spinPeierls transition was observed, 1) a gap appears below the critical temperature because of the lattice dimerization and the frustration. The other case with a gap is the XXZ chain with Ising anisotropy. CsCoCl 3 is known to be a typical 1D Ising-like antiferromagnet.2) One of the experimental means to measure the spin gap is the inelastic neutron scattering.3, 4) The neutron scattering brings us not only the information of the spin gap but also the whole excitation spectrum. 5,6) In this context, the dynamical structure factor (DSF) is a physical quantity to investigate carefully, because it is closely related with the experimental data detected by the neutron scattering.Besides connection with experiment, the study of dynamics is indispensable in order to understand the nature of elementary excitations in the system. To this end, it is desirable to find the exact expression of the DSF. Haldane and Zirnbauer 7) achieved this great work in the Haldane-Shastry (HS) model, 8,9) which is an isotropic spin model with exchange interaction proportional to the inverse square of the distance. Their result has the biggest merit that the picture of the elementary excitation is made simple. Recently, an integral representa- * E-mail: saiga@cmpt01.phys.tohoku.ac.jp tion of the exact DSF has been clarified for the nearestn...