Partial-state fidelity and quantum phase transitions induced by continuous level crossing

2008/05/28 by Ho-Man Kwok, Chun-Sing Ho, Shi-Jian Gu · 1 citation
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #Quantum many-body systems #quant-ph

paper · pdf · doi:10.1103/physreva.78.062302

published as Phys. Rev. A 78, 062302 (2008) · 5 pages, 4 figures

arxiv created 2008/05/28 · openalex publication_date 2008/12/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In quantum phase transitions induced by continuous level crossing, global-state fidelity drops to zero at every level crossing point, making finite-size scaling not applicable to study the criticality. In this paper, we calculate the partial-state fidelity in two models, i.e., the Lipkin-Meshkov-Glick (LMG) model and one-dimensional Heisenberg model. We show that it can spot the second-order phase transition point in the thermodynamic limit, where continuous level crossing occurs. The finite-size scaling shows the partial-state fidelity susceptibility diverges as N for the isotropic LMG model and N³ for the Heisenberg model.

Citations

• Validity of many-body approximation methods for a solvable model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Quantum Critical Scaling of the Geometric Tensors
• Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Ground-state fidelity in one-dimensional gapless models

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• Quantum instability and edge entanglement in the quasi-long-range order