A theory of quasiballistic spin transport
Abstract
A recent work [Mierzejewski et al., Phys. Rev. B 107, 045134 (2023)] observed “quasiballistic spin transport” – long-lived and transiently ballistic modes of the magnetization density – in numerical simulations of infinite-temperature XXZ chains with power-law exchange interactions. We develop an analytical theory of such quasiballistic spin transport. Previous work found that this effect was maximized along a specific locus in the space of model parameters, which interpolated smoothly between the integrable Haldane-Shastry and XX models and whose shape was estimated from numerics. We obtain an analytical estimate for the lifetime of the spin current and show that it has a unique maximum along a different locus, which interpolates more gradually between the two integrable points. We further rule out the existence of a conserved two-body operator that protects ballistic spin transport away from these integrable points by proving that a corresponding functional equation has no solutions. We discuss connections between our approach and an integrability-transport conjecture for spin.
Type
The correlator terms $\langle J(t)J(0) \rangle$ from the Drude weight give an accurate diagnosis of the ballistic transport. However, this is very difficult to calculate in principle. We pursue a more tractable version by minimizing the density of the rate of change of current, $\dot{\hat{J}}$.