Random matrix theory universality of current operators in spin-$S$ Heisenberg chains

Abstract:Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently narrow energy window, their statistical properties can be described by an unitarily invariant ensemble, and testable criteria have been introduced, which are based on the scaling behavior of free cumulants. In this paper, we investigate the conjecture numerically in translationally invariant Heisenberg spin chains with spin quantum number $S =\frac{1}{2},1,\frac{3}{2}$. Combining a quantum-typicality-based numerical method with the exploitation of the system's symmetries, we study the spin current operator and find clear evidence of consistency with the proposed criteria in chaotic cases. Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2601.10211 [cond-mat.stat-mech]

(or arXiv:2601.10211v2 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2601.10211 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. E, 114 , 024142 (2026)

https://doi.org/10.1103/fnmt-pp48 Focus to learn more DOI(s) linking to related resources

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