Absence of superdiffusion in certain random spin models

TL;DR

This paper investigates spin transport in a noisy spin-1/2 chain, demonstrating that regular diffusion persists despite strong noise, contrasting previous findings of superdiffusion in similar models.

Contribution

The study provides a perturbative analysis of spin dynamics under strong noise, showing the persistence of diffusion and offering insights beyond integrable models.

Findings

Regular diffusion persists at long times with an increased diffusion constant.

Operator dynamics can be analyzed using perturbation theory in the strong noise limit.

Finite time spin dynamics agree with matrix product operator simulations.

Abstract

The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability but the associated methods cannot be readily applied when integrability is broken. We examine spin transport in a spin-1/2 chain in which the exchange couplings fluctuate in space and time around a nonzero mean $J$, a model introduced by De Nardis et al. [Phys. Rev. Lett. 127, 057201 (2021)]. We show that operator dynamics in the strong noise limit at infinite temperature can be analyzed using conventional perturbation theory as an expansion in $J$. We find that regular diffusion persists at long times, albeit with an enhanced diffusion constant. The finite time spin dynamics is analyzed and compared with matrix product operator simulations.