Quasiballistic transport in long-range anisotropic Heisenberg model

TL;DR

This paper investigates quasiballistic spin transport in a long-range anisotropic Heisenberg model, revealing conditions under which transport is nearly ballistic and connecting it to known models with fully ballistic behavior.

Contribution

It demonstrates the emergence of quasiballistic transport in a long-range Heisenberg chain at specific anisotropy parameters, bridging free particle and Haldane-Shastry models.

Findings

Quasiballistic spin transport occurs near a specific anisotropy parameter.

Fermionic excitations do not decay over long timescales.

The results connect models with known ballistic transport properties.

Abstract

Purely ballistic transport is a rare feature even for integrable models. By numerically studying the Heisenberg chain with the power-law exchange, \mbox{$J\propto1/r^\alpha$}, where $r$ is a distance, we show that for spin anisotropy $\Delta \simeq \exp(-\alpha+2)$ the system exhibits a quasiballistic spin transport and the presence of fermionic excitation which do not decay up to extremely long times $\sim10^3/J$. This conclusion is reached on the base of the dynamics of spin domains, the dynamical spin conductivity, inspecting the matrix elements of the spin-current operator, and by the analysis of most conserved operators. Our results smoothly connects two models where fully ballistic transport is present: free particles with nearest-neighbor hopping and the isotropic Haldane-Shastry model.