It is of considerable theoretical significance to study the effects of impurity on spin dynamics of quantum spin systems. In this paper, the dynamical properties of the one-dimensional quantum Ising model with symmetric and asymmetric link-impurity are investigated by the recursion method, respectively. The autocorrelation function C(t)=¯⟨σxj(t)σxj(0)⟩ and the associated spectral density Φ(ω)=∫+∞−∞dteiωtC(t) are calculated. The Hamiltonian of the Ising model with link-impurity can be written as H=−12(Jj−1σxj−1σxj+Jjσxjσxj+1)−12JN∑i≠j,j−1σxiσxi+1−12BN∑iσzi.where J is the nearest-neighbor exchange coupling of the main spin chain, B denotes the external transverse magnetic field, σαi(α=x,y,z) are Pauli matrices at site i. The constant 1/2 is introduced for the convenience of theoretical deduction, and N is the number of spins. The so-called link-impurity Jj (Jj−1) is randomly introduced, which denotes the exchange coupling between the j th spin and the (j + 1)th spin (the (j – 1)th spin). The symmetric link-impurity and asymmetric link-impurity correspond to the case of Jj−1=Jj and Jj−1≠Jj, respectively. The periodic boundary conditions are assumed in the theoretical calculation.After introducing the link-impurity, the original competition between B and J in the pure Ising model is broken. The dynamic behavior of the system depends on synergistic effect of multiple factors, such as the mean spin coupling ˉJ between J and the link-impurity, the asymmetry degree between Jj−1 and Jj, and the strength of the external magnetic field. In calculation, the exchange couplings of the main spin chain are set to J≡1 to fix the energy scale. We first consider the effects of symmetric link-impurity. The reference values can be set to Jj−1=Jj<J (e.g. 0.4, 0.6 or 0.8) or Jj−1=Jj>J (e.g. 1.2, 1.6, 2.0), which are called weak or strong impurity coupling. When the magnetic field B⩾ (e.g., B = 1 , 1.5 or 2.0), it is found that the dynamic behavior of the system exhibits a crossover from a collective-mode behavior to a central-peak behavior as the impurity strength {J_{j - 1}} = {J_j} increases. Interestingly, for B \lt J (e.g. B = 0.4 or 0.7), there are two crossovers that are a collective-mode-like behavior to a double-peak behavior, then to a central-peak behavior as {J_{j - 1}} = {J_j} increases.For the case of asymmetric link-impurity, the impurity configuration is more complex. Using the cooperation between {J_{j - 1}} and {J_j} , more freedoms of regulation can be provided and the dynamical properties are more abundant. For the case of B \leqslant J (e.g. B = 0.5 , 1.0), the system tends to exhibit a collective-mode behavior when the mean spin coupling \bar J is weak, and a central-peak behavior when \bar J are strong. However, when the asymmetry between {J_{j - 1}} and {J_j} is obvious, the system tends to exhibit a double- or multi-peak behavior. For the case of B \gt J (e.g. B = 1.5 , 2.0), when \bar J is weak or the asymmetry between {J_{j - 1}} and {J_j} is not obvious, the system tends to exhibit a collective-mode behavior. When \bar J is strong, it tends to show a central-peak behavior. However, when the asymmetry between {J_{j - 1}} and {J_j} is evident, the bispectral feature (two spectral peaks appear at {\omega _1} \ne 0 and {\omega _2} \ne 0 ) dominates the dynamics. Under the regulating effect of link-impurities, the crossover between different dynamic behaviors can be easily realized, and it is easier to stimulate new dynamic modes, such as the double-peak behavior, the collective-mode-like behavior or bispectral feature one. The results in this work indicate that using link-impurity to manipulate the dynamics of quantum spin systems may be a new try.
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