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

TL;DR

This study analyzes quantum phase transitions in the U(5) to SO(6) region of the Interacting Boson Model using maximum likelihood estimation to characterize energy level statistics and chaos, introducing a new NNSD distribution.

Contribution

It introduces a novel NNSD distribution for better comparison with GUE and GOE ensembles and explores the universality of NNSD in the large boson number limit.

Findings

NNSD parameter depends on control parameter c_s

Transitional regions exhibit chaotic behavior

New NNSD distribution improves GUE and GOE comparison

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.