Multifractal mesoscopic fluctuations in the quantum dynamics of a spatially modulated chain

We investigate mesoscopic fluctuations in the quantum dynamics of a one-dimensional spin-1/2 chain composed of N spins, featuring alternating on-site energies and staggered nearest-neighbor coupling strengths. The coupling term corresponds to an exchange interaction between adjacent spins, playing the role of an effective hopping amplitude for spin excitations along the chain. This model provides a versatile platform to explore the interplay between quantum correlations, spatial modulation, and coherent transport. Using exact diagonalization, we follow the time evolution of an initially localized Gaussian wave packet by solving the time-dependent Schrödinger equation through the unitary time-evolution operator, and characterize its dynamics via the Loschmidt echo and the pairwise concurrence. We show that the spreading of the wave packet exhibits nontrivial behavior, strongly influenced by the alternating coupling pattern and the underlying modulation of the system. By analyzing the temporal fluctuations of these quantum-information observables, we identify clear signatures of multifractality, reflecting the mesoscopic nature of coherence fluctuations in finite-size systems with modulated interactions. Our results uncover rich dynamical regimes in which multifractal mesoscopic fluctuations emerge in standard quantum information measures due to the combined effects of spatial modulation, quantum interference, and finite-size constraints.