Entanglement entropy and Schmidt number as measures of delocalization of $\alpha$ clusters in one-dimensional nuclear systems

Abstract

We calculated the von Neumann entanglement entropy and the Schmidt number of one dimentional (1D) cluster states and showed that these are useful measures to estimate entanglement caused by delocalization of clusters. We analyze system size dependence of these entanglement measures in the linear-chain $n\alpha$ states given by Tohsaki-Horiuchi-Schuck-Röpke wave functions for 1D cluster gas states. We show that the Schmidt number is an almost equivalent measures to the von Neumann entanglement entropy when the delocalization of clusters occurs in the entire system but it shows different behaviors in a partially delocalized state containing localized clusters and delocalized ones. It means that the Rényi-2 entanglement entropy, which relates to the Schmidt number, is found to be almost equivalent to the von Neumann entanglement entropy for the full delocalized cluster system but it is less sensitive to the partially delocalized cluster system than the von Neumann entanglement entropy. We also propose a new entanglement measure which has a generalized form of the Schmidt number. Sensitivity of these measures of entanglement to the delocalization of clusters in low-density regions was discussed.

arXiv comment15 pages, 10 figures

References in corpus (20)

• Quantum entanglement
• Entanglement Entropy and Quantum Field Theory
• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Holographic Entanglement Entropy: An Overview
• Alpha cluster condensation in 12C and 16O
• Analysis of previous microscopic calculations for second $0^{+}$ state in ${}^{12}$C in terms of 3-alpha particle Bose-condensed state
• Essential entanglement for atomic and molecular physics
• Concepts of alpha-particle condensation
• Nonlocalized Clustering: A New Concept in Nuclear Cluster Structure Physics
• Entanglement of Local Operators in large N CFTs
• Description of 8Be as Deformed Gas-like Two-Alpha-Paricle States
• Quantum entanglement as an interpretation of bosonic character in composite two-particle systems
• One-dimensional $\alpha$ condensation of $\alpha$-linear-chain states in ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$
• Entanglement in composite bosons realized by deformed oscillators
• Entanglement and Composite Bosons
• Accuracy of BCS-based approximations for pairing in small Fermi systems
• What is "system": some decoherence-theory arguments
• Analysis of delocalization of clusters in linear-chain $\alpha$-cluster states with entanglement entropy
• Description of $\alpha$-cluster tail in ${}^8$Be and ${}^{20}$Ne: Delocalization of $\alpha$ cluster because of quantum penetration

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