Spin transport in disordered long-range interacting spin chain

TL;DR

This paper investigates spin transport in a disordered long-range interacting spin chain, confirming delocalization for certain interaction decay rates and identifying diffusive behavior with transient super-diffusive tails.

Contribution

It provides a numerically exact analysis of spin transport in disordered long-range systems, extending Griffiths' theory to these models and characterizing their transport regimes.

Findings

System is delocalized for $ ext{decay exponent} < 2$

Transport is diffusive for $ ext{decay exponent} > 3/2$

Transient super-diffusive tails observed in transport dynamics

Abstract

Using a numerically exact technique we study spin transport and the evolution of spin-density excitation profiles in a disordered spin-chain with long-range interactions, decaying as a power-law, $r^{-\alpha}$ with distance and $\alpha<2$. Our study confirms the prediction of recent theories that the system is delocalized in this parameters regime. Moreover we find that for $\alpha>3/2$ the underlying transport is diffusive with a transient super-diffusive tail, similarly to the situation in clean long-range systems. We generalize the Griffiths picture to long-range systems and show that it captures the essential properties of the exact dynamics.