Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory

Shinya Ae

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arXiv · 2605.01645

Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory

Shinya Ae

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Abstract

Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length $N$, the equal-time two-point spin correlation function is scaled up to $O(1/N)$. In the state where the ballistic spin transport decays at high temperature $T$, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to $1/T$ in the limit $T\to\infty$ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the $1/N$-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.

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Shinya Ae. 2026-05-02. Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory. https://arxiv.org/abs/2605.01645

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