Fidelity Susceptibility In The SU(2) And SU(1,1) Algebraic Structure Models

Now, the society has been high degree of information, people are looking forward to the quantum computers which are high-speed and energy-efficient. In the process of information transmission, the original information must be reduced. In the reduction of quantum information, quantum state must be involved in the conversion. As a closed quantum system, we can take the unitary transformation to complete this process. For the unitary transformation, one of the most important characteristic quantity is fidelity. With further research, people found a new tool - the fidelity susceptibility.We study the fidelity based on Lie algebraic method. We will obtained the exact expressions of fidelity susceptibilities in SU(2) and SU(1,1) algebraic structure models. The results obtained can be applied to one-body system and many-body system, such as a single spin model, single-mode squeeze harmonic oscillator model and BCS model etc. In terms of double-time Green-function method, our general conclusions are illustrated through two models which exhibit the fidelity susceptibilities at the finite temperature and T=0.