Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

2008/03/31 by Shuo Yang, Shi-Jian Gu, Chang-Pu Sun +1 · 14 citations
Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Anyon #Combinatorics #Condensed matter physics #Correlation function (quantum field theory) #Critical point (mathematics) #Function (biology) #Gapless playback #Geometry #Ground state #Honeycomb #Mathematics #Phase (matter) #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Topological quantum computer #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physreva.78.012304

published as Phys. Rev. A 78, 012304 (2008) · 7 pages, 6 figures

openalex publication_date 2008/07/02 · arxiv created 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped A phase with Abelian anyon excitations to a gapless B phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be 1/\ensuremathξ=2 sinh^\ensuremath-1[√2J_z\ensuremath-1/(1\ensuremath-J_z)], which diverges around the critical point J_z=(1/2)⁺.

Citations

• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Ground State Fidelity from Tensor Network Representations
• 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
• Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order
• String-net condensation: A physical mechanism for topological phases
• Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction
• Quantum Critical Scaling of the Geometric Tensors
• Ordering, metastability and phase transitions in two-dimensional systems
• Ground-state fidelity in one-dimensional gapless models
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond

Cited by

• Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits
• Revealing Chern number from quantum metric
• Entanglement modes and topological phase transitions in superconductors
• Reduced fidelity in the Kitaev honeycomb model
• Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond
• Boundary fidelity and entanglement in the symmetry protected topological phase of the SSH model
• Abelian and non-Abelian quantum geometric tensor
• Fidelity susceptibility near topological phase transitions in quantum walks
• Adiabatic perturbation theory and geometry of periodically-driven systems
• One- and two-dimensional quantum models: Quenches and the scaling of irreversible entropy
• Detecting topological order with ribbon operators
• Reduced fidelity and quantum phase transitions in spin-1/2 frustrated Heisenberg chains
• Reduced fidelity susceptibility and its finite-size scaling behaviors in the Lipkin-Meshkov-Glick model
• Linking phase transitions and quantum entanglement at arbitrary temperature