Spin transport in long-range interacting one-dimensional chain

TL;DR

This study investigates how long-range interactions affect spin transport in a one-dimensional chain, revealing distinct regimes of relaxation and transport behaviors depending on the decay exponent.

Contribution

It provides a detailed numerical analysis of spin transport regimes in long-range interacting quantum chains, highlighting the transition from instantaneous relaxation to mixed diffusive and superdiffusive transport.

Findings

For <1/2, spin excitations relax instantaneously in the thermodynamic limit.

For >1/2, spin transport exhibits both diffusive and superdiffusive characteristics.

For >3/2, the spin diffusion coefficient is finite, but transport is never purely diffusive.

Abstract

We numerically study spin transport and nonequilibrium spin-density profiles in a clean one-dimensional spin-chain with long-range interactions, decaying as a power-law,$r^{-\alpha}$ with distance. We find two distinct regimes of transport: for $\alpha<1/2$, spin excitations relax instantaneously in the thermodynamic limit, and for $\alpha>1/2$, spin transport combines both diffusive and superdiffusive features. We show that while for $\alpha>3/2$ the spin diffusion coefficient is finite, transport in the system is never strictly diffusive, contrary to corresponding classical systems.