保真率与量子相变

量子相变是量子多体理论中的一个重要概念，保真度则是量子信息学的重要概念.文章简单介绍了一个量子系统的基态对系统参量的响应，即保真率，在量子相变中的行为.作为理解量子相变的一个新的视角，保真度方法的优势在于它是一个纯粹的几何学量，所以在研究相变过程中不需要考虑任何预设的序参量.文章用通俗的语言介绍了基态保真度、保真率、量子绝热维度以及它们的物理意义.为便于理解，文章以Lipkin-Meshkov-Glick模型与Kitaev蜂巢模型为例，对保真率在这两个模型中的性质做了简单介绍.

Fidelity susceptibility and quantum phase transitions

Quantum phase transition is one of the most important issues in condensed matter physics, and quantum fidelity is an important concept emerging from quantum information theory. In this paper, we describe as simply as possible the role of fidelity and its leading term, i.e. the so-called fidelity susceptibility, in quantum phase transitions. As a purely geometric quantity, the key advantage of the fidelity approach is that no a priori knowledge of the order parameter is assumed. Specifically, we discuss definitions of the fidelity, the fidelity susceptibility, and the corresponding quantum adiabatic dimension, as well as their role in quantum phase transitions. We also use the Lipkin-Meshkov-Glick model and the Kitaev honeycomb model as examples to clarify these issues.