Dynamic scaling and Family-Vicsek universality in SU⁡(N) quantum spin chains

Moca, Cătălin Paşcu (author), Dóra, Balázs (author), Sticlet, Doru (author), Valli, Angelo (author), Prosen, Tomaž (author), Zaránd, Gergely (author)

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.

• Language: English
• Keywords: quantum mechanics, quantum quench, spin chains
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2026
• Number of pages: Str. L020405-1-L020405-6
• Numbering: Vol. 113, iss. 2
• PID: 20.500.12556/RUL-180866
• UDC: 530.145
• ISSN on article: 2469-9950
• DOI: 10.1103/434y-71cd
• COBISS.SI-ID: 272104195
• Publication date in RUL: 18.03.2026

Record is a part of a journal

• Title: Physical review
• Publisher: American Physical Society
• ISSN: 2469-9950
• COBISS.SI-ID: 2997348

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, kvantne spinske verige