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.