Does Heisenberg-chain superdiffusion survive symmetric integrability-breaking perturbations? · revision history

Revision 2

Accepted · core change · record

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Title · changed
Revision 1: Does Heisenberg-chain superdiffusion survive symmetric integrability-breaking perturbations
Revision 2: Does Heisenberg-chain superdiffusion survive symmetric integrability-breaking perturbations?
Plain
In the solvable Heisenberg spin chain, magnetization spreads faster than ordinary diffusion. If the chain is perturbed so that it is no longer solvable but keeps its rotation symmetry, it is unclear whether the fast spreading persists forever or eventually becomes ordinary diffusion.
Precise · changed · core
Revision 1: Take $H = H_{\mathrm{XXX}} + g V$ with $V$ local, integrability breaking and $\mathrm{SU}(2)$ invariant (e.g. $V = \operatorname{sum}_i S_i . S_{i+2}$), at infinite temperature and zero magnetization. De Nardis, Gopalakrishnan, Vasseur, Ware (PRL 127, 057201, 2021) argued that large spin-carrying quasiparticles survive, giving spin conductivity $\sigma(\omega) \sim \omega^{-1/3}$ at low frequency instead of a finite DC value, while perturbations breaking $\mathrm{SU}(2)$ restore diffusion. Determine the low-frequency form of $\sigma(\omega)$ in the quantum chain, i.e. whether the spin diffusion constant is finite. Answer: finite $D(g)$ or divergent, with the exponent.
Revision 2: Take $H = H_{\mathrm{XXX}} + g V$ with $V$ local, integrability breaking and $\mathrm{SU}(2)$ invariant (e.g. $V = \sum_i S_i . S_{i+2}$), at infinite temperature and zero magnetization. De Nardis, Gopalakrishnan, Vasseur, Ware (PRL 127, 057201, 2021) argued that large spin-carrying quasiparticles survive, giving spin conductivity $\sigma(\omega) \sim \omega^{-1/3}$ at low frequency instead of a finite DC value, while perturbations breaking $\mathrm{SU}(2)$ restore diffusion. Determine the low-frequency form of $\sigma(\omega)$ in the quantum chain, i.e. whether the spin diffusion constant is finite. Answer: finite $D(g)$ or divergent, with the exponent.
Settled by
Real-time computation of the spin current correlator in the perturbed quantum chain at times long enough to distinguish $\omega^{-1/3}$ from a finite DC limit, for at least two values of $g$.
Kind
well-posed
Answer type
yes-no
References
(empty)
Literature status
contested
Status note
Kinetic theory predicts persistence (2021), while in the nonintegrable classical Heisenberg chain superdiffusion lasts a time diverging as a power of 1/T but finite (McRoberts and Moessner, PRL 133, 256301, 2024); long-time quantum results are lacking.
Posed since
2021

Decisions