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

Abstract

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 quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.

4 pages, 5 figures, version published in Phys. Rev. E

References in corpus (5)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Quantum fidelity and quantum phase transitions in matrix product states
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Entanglement in the Majumdar-Ghosh model

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