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arXiv:1106.2497

Level spacing of U(5) \leftrightarrow SO(6) transitional region with maximum likelihood estimation method

Jafarizadeh, N. Fouladic, H. Sabric, B. Rashidian Maleki

Published Jun 13, 2011• 0 citations
arXivHTMLPDF

Abstract

In this paper,a systematic study of quantum phase transition within U(5) \leftrightarrow SO(6) limits is presented in terms of infinite dimensional Algebraic technique in the IBM framework. Energy level statistics are investigated with Maximum Likelihood Estimation (MLE) method in order to characterize transitional region. Eigenvalues of these systems are obtained by solving Bethe-Ansatz equations with least square fitting processes to experimental data to obtain constants of Hamiltonian. Our obtained results verify the dependence of Nearest Neighbor Spacing Distribution's (NNSD) parameter to control parameter (c_{s}) and also display chaotic behavior of transitional regions in comparing with both limits. In order to compare our results for two limits with both GUE and GOE ensembles, we have suggested a new NNSD distribution and have obtained better KLD distances for the new distribution in compared with others in both limits. Also in the case of N\to\infty, the total boson number dependence displays the universality behavior, namely NNSD tends to Poisson limit for every values of control parameter.

DOI
10.48550/arxiv.1106.2497

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In this paper,a systematic study of quantum phase transition within U(5) \leftrightarrow SO(6) limits is presented in terms of infinite dimensional Algebraic technique in the IBM framework. Energy level statistics are investigated with Maximum Likelihood Estimation (MLE) method in order to characterize transitional region. Eigenvalues of these systems are obtained by solving Bethe-Ansatz equations with least square fitting processes to experimental data to obtain constants of Hamiltonian. Our obtained results verify the dependence of Nearest Neighbor Spacing Distribution's (NNSD) parameter to control parameter (c_{s}) and also display chaotic behavior of transitional regions in comparing with both limits. In order to compare our results for two limits with both GUE and GOE ensembles, we have suggested a new NNSD distribution and have obtained better KLD distances for the new distribution in compared with others in both limits. Also in the case of N\to\infty, the total boson number dependence displays the universality behavior, namely NNSD tends to Poisson limit for every values of control parameter.
The level statistics of SU(3)-SU(3)* transitional region of IBM is described by the nearest neighbor spacing distribution statistics. The energy levels are determined by using the SO(6)representation of eigenstates. By employing the MLE technique, the parameter of Abul-Magd distribution is estimated where suggest less regular dynamics for transitional region in compare to dynamical symmetry limits. Also, the O(6)dynamical symmetry which is known as the critical point of this transitional region, describes a deviation to more regular dynamics.
Abstract The spectral fluctuations and transition intensity fluctuations in the excited-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by adopting three statistical measures, including the nearest neighbor level spacing distribution P ( S ) measuring the chaoticity (regularity) in energy spectra, the Δ 3 ( L ) statistics of Dyson and Mehta measuring the spectral rigidity and the intensity distribution P ( y ) measuring the chaoticity (regularity) in B ( E 0) transitions. The results indicate that that the ESQPT as a function of the excitation energy may occur as a transition from regular (or semiregular) to highly chaotic if only the associated whole spectrum is chaotic, which fits most of the deformed situations in the IBM including those in the U(5)–SU(3) and SU(3)–O(6) transitional regions. Otherwise, the ESQPT will appear as a transition from regular (or semiregular) to regular such as the cases in the U(5)–O(6) transitional region or those on the ‘Alhassid–Whelan arc’, which represents a nearly regular parameter region connecting the U(5) and SU(3) limits in the IBM.
Analysis of the U(5)↔SU(3)U(5)\leftrightarrow SU(3)U(5)↔SU(3) transitional region from an entanglement-based perspective
The degree of entanglement between components of a bipartite system can serve as a useful criterion for studying Quantum Phase Transitions (QPT). The von Neumann entropy and generalized concurrence serve as measures, while Schmidt number and Schmidt gap are quantifiers; together, they are key tools for identifying QPT. Using these tools, we have examined the QPT in the [Formula: see text] region within the first version of the semiclassical approximation of the Interacting Boson Model (IBM-1). Additionally, the Kullback-Leibler divergence (KLD) was employed as a criterion to compare two probability distribution functions in order to identify the transition region and the critical point. The theoretical results indicated that the Schmidt number and Schmidt gap, the von Neumann entropy, generalized concurrence, and the KLD can characterize the transition behavior and critical point (X(5)) in this region. To verify these results in real nuclei, the Dysprosium isotopic chain was selected. Using the suggested entanglement measures, the symmetry limits and the critical point were identified. The results obtained are fully consistent with experimental evidence.
We study the energy level statistics of the states in U(5) and O(6) dynamical symmetries of the interacting boson model and the high spin states with backbending in U(5) symmetry. In the calculations, the degeneracy resulting from the additional quantum number is eliminated manually. The calculated results indicate that the finite boson number N effect is prominent. When N has a value close to a realistic one, increasing the interaction strength of subgroup O(5) makes the statistics vary from Poisson type to Gaussian orthogonal ensemble type and further recover to Poisson type. However, in the case of $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ they all tend to be Poisson type. The fluctuation property of the energy levels with backbending in high spin states in U(5) symmetry involves a signal of shape-phase transition between spherical vibration and axial rotation.
We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd- A nucleus using the interacting boson–fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (Δ 3 ) are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SO B (5) and SO BF (5) and the spin play important roles in the energy level statistics, however, along with the increase of N , the statistics distribution would tend to be in Poisson form.
We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd-A nucleus using the interacting boson-fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (△3)are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SOB(5) and SOBF(5)and the spin play important roles in the energy level statistics, however, along with the increase of N, the statistics distribution would tend to be in Poisson form.