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

Abstract

The entanglement entropy of s and d bosons in the framework of Interacting Boson Model -1 (IBM-1) has been obtained using consistent-Q formalism and semiclassical approximation. This has been possible by using Schmidt decomposition and expressing s and d bosons entanglement entropy in terms of Schmidt numbers. In this research, a simple method in the framework of IBM-1 has been presented for deriving the entanglement entropy in the Casten triangle. The results indicated that the entanglement entropy is sensitive to the shape-phase transition in the various regions of the Casten triangle. It was demonstrated that the entanglement entropy of s and d bosons in the semiclassical approximation depends only on the values of the deformation parameter (β) and is independent of the angular parameter (γ). Also, the entanglement entropy between s and d bosons reaches its maximum value in the O(6) limit, while it decreases in the SU(3) limit, and reaches zero in the U(5) limit. Based on the results obtained via Schmidt decomposition, it is shown that the probability distribution functions of the number of s bosons in IBM-1 are the binomial distributions. For NB≫1, it was proved that the distribution function in the SU(3), O(6) and SU(3)‾ limits is the Gaussian, and in the U(5) limit is the Poissonian.