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

2007/06/30 by Shu Chen, Li Wang, Shi-Jian Gu +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Strong Light-Matter Interactions #cond-mat.other

paper · pdf · doi:10.1103/physreve.76.061108

published as Phys. Rev. E 76, 061108 (2007) · 4 pages, 5 figures, version published in Phys. Rev. E

openalex publication_date 2007/12/07 · arxiv created 2007/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J1-J2 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 J1-J2 model cannot 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.

Citations

• On Next-Nearest-Neighbor Interaction in Linear Chain. I
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• The critical properties of the two-dimensional xy model
• Ordering, metastability and phase transitions in two-dimensional systems

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