Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction

Shu Chen, Li Wang, Shi-Jian Gu, Yupeng Wang
2007 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
more » ... antum transition can be well characterized by the fidelity of the first excited state even for a small-size system.
doi:10.1103/physreve.76.061108 pmid:18233815 fatcat:y43yf7gacvdqpld4yyyr5rbzvq