20.500.12556/RUL-180866 Dynamic scaling and Family-Vicsek universality in SU⁡(N) quantum spin chains The Family-Vicsek scaling is a fundamental framework for understanding surface growth in nonequilibrium classical systems, providing a universal description of temporal surface roughness evolution. Whether such scaling extends to strongly correlated quantum many-body systems—where dynamics are governed by unitarity, conservation laws, and quantum statistics—remains an open question. Here, we investigate the infinite-temperature dynamics of one-dimensional $SU (N)$ spin chains, focusing on the well-known $SU (2)$ XXZ model and the $SU (3)$ Izergin-Korepin model. We compute the quantum analog of classical surface roughness using the second cumulant of spin fluctuations and demonstrate Family-Vicsek scaling with respect to time and subsystem size. Crucially, we show that the scaling behavior is controlled by both integrability and non-Abelian global symmetries. We identify distinct transport regimes characterized by the dynamical exponent $z$: (i) ballistic transport with $z=1$, (ii) superdiffusive transport with the Kardar-Parisi-Zhang exponent $z=3/2$, and (iii) diffusive transport with the Edwards-Wilkinson exponent $z=2$. Notably, breaking integrability always drives the system into the diffusive regime. Our results demonstrate that Family-Vicsek scaling extends beyond classical systems, and emerges across quantum many-body models with $SU (N)$ symmetry. quantum mechanics quantum quench spin chains kvantna mehanika kvantne spinske verige true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-18 12:27:12 2026-03-18 12:27:13 2026-04-13 08:19:50 0000-00-00 00:00:00 2026 0 0 Str. L020405-1-L020405-6 iss. 2 Vol. 113 2026 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 530.145 2469-9950 10.1103/434y-71cd 272104195 2503.21454v1.pdf 2503.21454v1.pdf 1 21FFAD167CD9646E4C3F702FFBF53313 95d28cbc3ec4081b07a882c8f14fabe766d7e1ae74357c4df10ebf63d28d282a eb804f4f-22be-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=230790 https://journals.aps.org/prb/abstract/10.1103/434y-71cd 0 f3b0eee5-22be-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=230791 Fakulteta za matematiko in fiziko 0 0 0