We investigate the generation of non-stabilizerness, or magic, in a
multi-particle quantum walk by analyzing the time evolution of the stabilizer
R\'enyi entropy
M2. Our study considers both single- and two-particle
quantum walks in the framework of the XXZ Heisenberg model with varying
interaction strengths. We demonstrate that the spread of magic follows the
light-cone structure dictated by the system's dynamics, with distinct behaviors
emerging in the easy-plane (
\Delta < 1) and easy-axis (
\Delta > 1) regimes.
For
\Delta < 1, magic generation is primarily governed by single-particle
dynamics, while for
\Delta > 1, doublon propagation dominates, resulting in a
significantly slower growth of
M2. Furthermore, the magic exhibits
logarithmic growth in time for both one and two-particle dynamics.
Additionally, by examining the Pauli spectrum, we show that the statistical
distribution of level spacings exhibits Poissonian behavior, independent of
interaction strength or particle number. Our results shed light on the role of
interactions on magic generation in a many-body system.