The role of next-nearest-neighbor interactions in the dynamics of the spin-1/2 disordered Ising ladder in random transverse field

The spin-1/2 quantum disordered Ising ladder, in the presence of a random transverse magnetic field, is studied using the method of recurrence relations in the high temperature limit. The ladder has homogeneous nearest-neighbor (NN) and homogeneous next-nearest-neighbor (NNN) interactions along the two side rails. The two side rails are coupled by disordered rung interactions. Using the recurrence relations method (RRM) in the high-temperature limit, we calculate the first four recurrants exactly and employ a linear extrapolation procedure to generate any necessary number of additional recurrants. In particular, the time autocorrelation function for the z component of the dynamic spin variable and its corresponding spectral function were calculated. The dynamics of both quantities depend on the values of the theoretical parameters as well as on the disorder type, and can change from central peak at low fields to collective-mode behavior at higher fields. Notably, the spectral functions exhibited a distinct change in behavior as the NNN coupling strength was varied, suggesting a transition in the dynamical response of the system. An interesting case of rung-transverse-field correlated randomness is also analyzed. In general, NNN interactions play an important role in maintaining temporal coherence, as demonstrated by the slower decay of the spin autocorrelation function and the persistence of the central peak in the spectral function, even under a strong external magnetic field.