Non-stabilizerness generation in a multi-particle quantum walk

Abstract: 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 $M_2$. 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 $M_2$. 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.