Localization and magnetic field effects in Heisenberg chains with generalized exponentially correlated disorder

We examine the properties of the one-magnon eigenstates in a Heisenberg chain with correlated disorder in the presence of a magnetic field that increases linearly along the chain. The disorder distribution is tailored to have intrinsic generalized exponential correlations. We further analyze the dynamic localization of an initial wave packet and discuss how it is influenced by the correlations and the strength of the magnetic field. We find that localized eigenstates are predominant when the correlated disorder is characterized by a slower dependence of the effective correlation length on the system size. In contrast, when the effective correlation length increases at least with the square root of the system size, low-energy eigenmodes undergo a transition to nearly delocalized modes. We go further to analyze the impact of a linearly varying magnetic field on the system dynamics. An initial Gaussian wave packet is shown to exhibit dynamic localization, characterized by an oscillatory behavior reminiscent of Bloch oscillations at specific correlation levels, before being damped in the long time limit. Our findings advances the understanding of localization and transport properties in the field of coherent magnonics as contributes to the design of correlated disordered media.