Coherent transport over an explosive percolation lattice

TL;DR

This paper studies how correlated bond growth in a percolation lattice affects quantum transport efficiency, revealing that certain correlations can enhance or reduce transport, with implications for localization properties.

Contribution

It introduces a novel analysis of coherent transport on correlated explosive percolation lattices, highlighting how correlation strength influences transport efficiency and localization.

Findings

Optimal correlation strength can enhance transport efficiency.

Higher correlation strengths may reduce transport efficiency.

Structural differences due to correlations affect localization properties.

Abstract

We investigate coherent transport over a finite square lattice in which the growth of bond percolation clusters are subjected to an Achlioptas type selection process, i.e., whether a bond will be placed or not depends on the sizes of clusters it may potentially connect. Different than the standard percolation where the growth of discrete clusters are completely random, clusters in this case grow in correlation with one another. We show that certain values of correlation strength, if chosen in a way to suppress the growth of the largest cluster which actually results in an explosive growth later on, may lead to more efficient transports than in the case of standard percolation, satisfied that certain fraction of total possible bonds are present in the lattice. In this case transport efficiency increases as a power function of bond fraction in the vicinity of where effective transport begins. It turns out that the higher correlation strengths may also reduce the efficiency as well. We also compare our results with those of the incoherent transport and examine the average spreading of eigenstates for different bond fractions. In this way, we demonstrate that structural differences of discrete clusters due to different correlations result in different localization properties.