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Nuclear Physics A

Entanglement entropy approach for examining quantum phase transition in the framework of semiclassical approximation: Testing its validity in Casten triangle

Maryam Ghapanvari, M. A. Jafarizadeh, M Sayedi, Narjes Amiri

Published Sep 17, 2024• 6 citations
Publisher
DOI
10.1016/j.nuclphysa.2024.122960

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In this research, the quantum phase transition (QPT) in the Casten pyramid has been investigated using entanglement entropy. Energy surfaces and the entanglement entropy have been obtained within the framework of semi-classical approximation interacting boson model-2 (IBM-2) using Schmidt decomposition and coherent states formalism. The results showed that the entanglement entropy is a suitable and efficient tool for investigating QPT and determining critical points in the connected pathes to the Uπν(5){U_{\pi \nu }}\left( 5\right)Uπν​(5) limit, and pathes of SUπν(3)↔Oπν(6)↔SUπν(3)‾S{U_{\pi \nu }}\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{S{U_{\pi \nu }}\left( 3 \right) }SUπν​(3)↔Oπν​(6)↔SUπν​(3)​ and SUπν∗(3)↔Oπν(6)↔SUπν∗(3)‾SU_{\pi \nu }^*\left( 3 \right) \leftrightarrow {O_{\pi \nu }}\left( 6 \right) \leftrightarrow \overline{SU_{\pi \nu }^*\left( 3 \right) }SUπν∗​(3)↔Oπν​(6)↔SUπν∗​(3)​ . The description of QPT using numerical analysis of energy surfaces confirms the results of entanglement entropy.
A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X (5), -X (5), and E (5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the ( η, χ ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed.
The evolution of system observables at critical points of quantum phase transitions in atomic nuclei is explored within the context of the interacting boson model-1. The evolution of energies and transition strengths in the ground state band at the infinite-size critical point are examined with respect to system size. Properties of first-order phase transitions away from the U(5)-SU(3) leg of the Casten triangle are examined, and the effects of angular momentum on the evolution of system observables at the critical point are investigated for the first time.