Superdiffusive transport on lattices with nodal impurities

TL;DR

This paper demonstrates that 1D lattice models with nodal impurities exhibit superdiffusive transport, characterized by a specific dynamical exponent, and explores how time reversal symmetry affects this behavior.

Contribution

It introduces the concept of nodal impurities in 1D lattices and calculates the resulting superdiffusive transport exponents, expanding understanding of disorder effects without interactions.

Findings

Superdiffusive transport occurs with nodal impurities in 1D lattices.

The dynamical exponent z depends on the node order n, with z=4n/(4n-1).

Time reversal symmetry can increase z to 8n/(8n-1).

Abstract

We show that 1D lattice models exhibit superdiffusive transport in the presence of random "nodal impurities" in the absence of interaction. Here a nodal impurity is defined as a localized state, the wave function of which has zeros (nodes) in momentum space. The dynamics exponent $z$, a defining quantity for transport behaviors, is computed to establish this result. To be specific, in a disordered system having only nodal impurities, the dynamical exponent $z=4n/(4n-1)$ where $n$ is the order of the node. If the system has time reversal, the nodes appear in pairs and the dynamical exponent can be enhanced to $z=8n/(8n-1)$. As $1<z<2$, both cases indicate superdiffusive transport.