Spin dynamics of the quantum XY chain and ladder in a random field

We investigate the Hamiltonian dynamics of two low-dimensional quantum spin systems in a random field, at the infinite-temperature limit: the XY chain and the two-leg XY ladder with interchain Ising interactions. We determine the longitudinal spin autocorrelation functions of the spin-12XY chain and ladder in the presence of disordered fields by using the method of recurrence relations. The first six basis vectors for the chain and the first four basis vectors for the ladder of the dynamic Hilbert spaces of σjz(t), as well as the corresponding recurrents and moments of the time-dependent autocorrelation function, are analytically computed for bimodal distributions of the fields. We did find a remarkable result in the disordered models. Cases with a fraction of p sites under field BB and a fraction of 1−p sites under the field BA have the same longitudinal dynamics as those with p sites under field BA and 1−p sites under the field BB. We also find that both the XY chain and the two-leg XY ladder with Ising interchain coupling in the presence of random fields are sensitive to the percentage of disorder but not to the intensity of the fields.