Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction
Shu Chen, Li Wang, Shi-Jian Gu, Yupeng Wang
Physical Review E
In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J_1-J_2 model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the J_1-J_2 model can not be well characterized by the ground state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the
... antum transition can be well characterized by the fidelity of the first excited state even for a small-size system.