Research Paper: Phase Transition Analysis in the Combined PRBM- RD Model Using Quantum Indicators

In this study, we explore the localization and transport behaviors of a one-dimensional system using a hybrid model that combines the Power-Law Random Banded Matrix (PRBM) model and the Random Dimer (RD) model. The primary objective of this research is to examine phase transitions and the influence of system parameters on quantum states. To achieve a precise analysis of these transitions, we utilize quantities such as the participation ratio and the energy level spacing ratio, each providing valuable insights into the system's dynamics. The results indicate that by varying parameters α and , the transition from extended to localized states can be effectively controlled. Specifically, α emerges as a critical factor in determining phase transitions, playing a key role in inducing phase shifts. This hybrid model, with its capacity for accurate simulation, enables a comprehensive examination of quantum behaviors in complex systems and paves the way for future studies on the effects of disorder and random variations in quantum phase transitions. This research establishes a robust foundation for deeper understanding of phase transition mechanisms in disordered systems.