Quantum State Evolution and Berry Potentials at Exceptional Points and Quantum Phase Transitions

Abstract: The behavior of quantum states at exceptional points and at critical points associated with quantum phase transitions is intriguing yet puzzling. In this study, we present an alternative method for obtaining the Berry potentials using the evolution generator along the parameter induced dimension and demonstrate that they are singular at these critical points. Although these singularities may appear to indicate a breakdown in quantum state evolution, we show that the information carried by quantum states evolving across these critical points is not destroyed. Specifically, when the evolution generator of the full Hilbert space bundle is taken into account, the quantum states remain insensitive to the critical points. In physical terms, it's similar to the classical image of an object smoothly passing through a black hole's event horizon. Further similarities between exceptional points and quantum phase transitions are explored in this work.