Analysis of delocalization of clusters in linear-chain $\alpha$-cluster states with entanglement entropy

TL;DR

This paper explores how entanglement entropy can quantify the delocalization of alpha clusters in linear-chain states, revealing spatial regions of delocalization and differences between localized and delocalized wave functions.

Contribution

It demonstrates that entanglement entropy effectively measures cluster delocalization in 1D alpha-cluster states, with analysis of spatial distribution and effects of system size.

Findings

Delocalization occurs mainly in low-density tail regions due to Pauli blocking.

Entanglement entropy distinguishes localized from delocalized cluster wave functions.

Larger systems show delocalization across the entire system.

Abstract

I investigate entanglement entropy of one dimension (1D) cluster states to discuss the delocalization of clusters in linear-chain $3\alpha$- and $4\alpha$-cluster states. In analysis of entanglement entropy of 1D Tohsaki-Horiuchi-Schuck-R\"opke (THSR) and Brink-Bloch cluster wave functions, I show clear differences in the entanglement entropy between localized cluster wave functions and delocalized cluster wave functions. In order to clarify spatial regions where the entanglement entropy is generated by the delocalization of clusters, I analyze the spatial distribution of entanglement entropy. In the linear-chain $3\alpha$ cluster state, the delocalization occurs dominantly in a low-density tail region while it is relatively suppressed in an inner region because of Pauli blocking effect between clusters. In the linear-chain 4$\alpha$ state having a larger system size than the linear-chain $3\alpha$ state, the delocalization occurs in the whole system. The entanglement entropy is found to be a measure of the delocalization of clusters in the 1D cluster systems.