Reduced fidelity and quantum phase transitions in spin-1/2 frustrated Heisenberg chains

2008/08/31 by Heng-Na Xiong, Jian Ma, Yan Wang +2
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Class (philosophy) #Fidelity #Phase (matter) #Phase transition #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum phase transition #Quantum phases #Spin (aerodynamics) #quant-ph

paper · pdf · doi:10.1088/1751-8113/42/6/065304

6 pages, 2 figures

openalex publication_date 2009/01/15 · arxiv created 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We use reduced fidelity to characterize quantum phase transitions in the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain with frustration. For the ground state and the low-lying excited states, explicit results of the reduced fidelities between the nearest-neighbor and next-nearest-neighbor spins are given in both the even-size and odd-size cases. We find the reduced fidelity is an effective tool in detecting the quantum phase transitions associated with level crossings for the finite-size systems. Interestingly, the reduced fidelity between next-nearest-neighbor spins is evidently more sensitive at the quantum phase transition points than the nearest-neighbor case. Moreover, the reduced fidelity of the low-lying excited states is a good indicator both for the first-order and infinite-order quantum phase transitions of the system.

Citations

• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Fidelity for Mixed Quantum States
• On Next-Nearest-Neighbor Interaction in Linear Chain. I
• Ground State Fidelity from Tensor Network Representations
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb 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
• The critical properties of the two-dimensional xy model
• Spin fluctuations in the quasi-two-dimensional Heisenberg ferromagnetGdI2studied by electron spin resonance
• Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction
• Ordering, metastability and phase transitions in two-dimensional systems
• Ground-state fidelity in one-dimensional gapless models