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

TL;DR

This study numerically investigates the universality of current operators in spin-$S$ Heisenberg chains, providing evidence that their statistical properties align with random matrix theory predictions in quantum chaotic regimes.

Contribution

It offers the first numerical validation of RMT universality for current operators in spin-$S$ Heisenberg chains across different spins, using symmetry-exploited quantum-typicality methods.

Findings

Evidence of RMT universality in chaotic spin chains

Consistency of current operator statistics with RMT predictions

Support for the conjecture of universal observable properties in quantum chaos

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.