Local quantum fisher information and quantum phase transitions in the XY spin-1/2 chain

The article delves into the intricate relationship between local quantum Fisher information (LQFI) and quantum phase transitions (QPTs) within the XY spin-1/2 chain. It begins by establishing the foundational role of quantum Fisher information (QFI) in quantum metrology, emphasizing its ability to quantify information and enhance measurement precision. The study then focuses on LQFI, a variant that examines specific subsystems within a broader quantum system, and its potential to detect QPTs. The research explores how LQFI varies with distance between spins, anisotropy parameters, temperature, and transverse magnetic fields, revealing critical points associated with QPTs. The article presents detailed analytical expressions and numerical simulations, illustrating the behavior of LQFI under different conditions. It highlights the unique cusp-like and divergent behaviors of LQFI at critical points, demonstrating its effectiveness as a QPT detector. Additionally, the study discusses the influence of thermal fluctuations on LQFI, providing a nuanced understanding of its application in real-world quantum systems. The findings suggest that LQFI is not only a tool for evaluating measurement accuracy but also a powerful detector of QPTs, offering valuable insights for advancing quantum metrology and phase transition studies.