Effects of random longitudinal magnetic field on dynamics of one-dimensional quantum Ising model

The dynamical properties of quantum spin systems are a hot topic of research in statistical and condensed matter physics. In this paper, the dynamics of one-dimensional quantum Ising model with both transverse and longitudinal magnetic field (LMF) is investigated by the recursion method. The time-dependent spin autocorrelation function G(t) = <(<sigma(x)(j)(t))sigma(x(0)>)(j)over bar>and corresponding spectral density Phi(omega) are calculated. The Hamiltonian of the model system can be written as H = -1/2J Sigma(N)(i)sigma(x)(i)sigma(x)(i+1) 1/2 Sigma B-N(i)i(x)sigma(x)(i) - 1/2 Sigma B-N(i)i(z)sigma(z)(i) This work focuses mainly on the effects of LMF (B-i(x)) on spin dynamics of the Ising system, and both uniform LMF and random LMF are considered respectively. Without loss of generality, the transverse magnetic field is set in the numerical calculation, which fixes the energy scale. The results show that the uniform LMF can induce crossovers between different dynamical behaviors (e.g. independent spins precessing, collective-mode behavior or central-peak behavior) and drive multiple vibrational modes (multiple-peaked behavior) when spin interaction (J) is weak. However, the effect of uniform LMF is not obvious when spin interaction is strong. For the case of random LMF, the effects of bimodal-type and Gaussiantype random LMF are investigated, respectively. The dynamical results under the two types of random LMFs are quite different and highly dependent on many factors, such as the mean values (B-1, B-2, and B-x) or the standard deviation (sigma) of random distributions. The nonsymmetric bimodal-type random LMF (B-1 not equal B-2) may induce new vibrational modes easily. The dynamical behaviors under the Gaussian-type random LMF are more abundant than under the bimodal-type random LMF. When is small, the system undergoes two crossovers: from a collective-mode behavior to a double-peaked behavior, and then to a central-peak behavior as the mean value B-x increases. However, when is large, the system presents only a central-peak behavior. For both cases of uniform LMF and random LMF, it is found that the central-peak behavior of the system is maintained when the proportion of LMF is large. This conclusion can be generalized that the emergence of noncommutative terms (noncommutative with the transverse-field term) in Hamiltonian will enhance the central peak behavior. Therefore, noncommutative terms, such as next-nearest-neighbor spin interactions, Dzyaloshinskii-Moryia interactions, impurities, four-spin interactions, etc., can be added to the system Hamiltonian to modulate the dynamical properties. This provides a new direction for the future study of spin dynamics.