Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

Abstract

We study the scaling behavior of the fidelity ($F$) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of $F$ for an anisotropic quantum critical point for both thermodynamic and non-thermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of $F$ inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate $F$ through the overlap between the ground states for angle of rotation $\eta$ and $\eta +d\eta$, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

10 pages, 8 figures

References in corpus (27)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Quantum discord and quantum phase transition in spin chains
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Geometric phases and criticality in spin chain systems
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Exact results for quench dynamics and defect production in a two-dimensional model
• Ground state fidelity from tensor network representations
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Long-distance entanglement in spin systems
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Oscillating fidelity susceptibility near a quantum multicritical point
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Scaling of ground state fidelity in the thermodynamic limit: XY model and beyond
• Reduced fidelity in topological quantum phase transitions
• Geometric phases and quantum phase transitions
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Geometric phases and criticality in spin systems
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Quantum Discord in a spin-1/2 transverse XY Chain Following a Quench
• Path dependent scaling of geometric phase near a quantum multi-critical point

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• Numerical studies of ground state fidelity of the Bose-Hubbard model
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• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
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• Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature
• Role of marginality in quantum fidelity and Loschmidt echo: Dirac points in 2-D
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Dynamics of Majorana zero modes across hybrid Kitaev chain