Quantum correlations and entanglement in a Kitaev-type spin chain

Abstract

The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical point. But peculiarly in this model, the entanglement measures do not show any singular behavior in the vicinity of the critical point, as seen in the transverse Ising model ground state and related models. We have investigated different correlation measures analytically, that have been used for many solvable spin systems to track a quantum critical point. We compute the pair concurrence measure of entanglement, the pair quantum discord to track the quantum correlations, and a global entanglement measure and a multi-species entanglement measure to investigate multi-party entanglement, both analytically and numerically. The nearest-neighbor concurrence shows a peak structure as a function of magnetic field, near the critical point, for various values of the ratio of interaction strengths, but its derivative does not show a singular behavior close to the critical point. A similar behavior is shown by the quantum discord and the global entanglement. The multi-species entanglement shows the most-pronounced signature of the critical point, in its first-order derivative, though the entanglement and its derivatives have a smooth behavior in the critical region.

arXiv comment14 pagers, 7 figures

References in corpus (20)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Fault-tolerant quantum computation by anyons
• Introducing Quantum Discord
• Topological entanglement entropy
• Scaling of Entanglement close to a Quantum Phase Transitions
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Global entanglement in multiparticle systems
• Quantum discord and quantum phase transition in spin chains
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems
• Topological states and braiding statistics using quantum circuits
• Entanglement entropy in the Long-Range Kitaev chain
• Local entanglement and quantum phase transition in 1D transverse field Ising model
• Quantum information approach to the quantum phase transition in the Kitaev honeycomb model
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• Reverse quenching in a one-dimensional Kitaev model
• Manipulating unpaired Majorana fermions in a quantum spin chain
• Entanglement and Majorana edge states in the Kitaev model
• Block entropy for Kitaev-type spin chains in a transverse field

Cited by in corpus (13)

• Unveiling the phase diagram of a bond-alternating spin-$\frac{1}{2}$ $K$-$\Gamma$ chain
• Global entanglement in a topological quantum phase transition
• Exact zero modes in a quantum compass chain under inhomogeneous transverse fields
• Entanglement measures of Majorana bound states
• Insights into the Anisotropic Spin-$S$ Kitaev Chain
• Spin dynamics of the generalized quantum spin compass chain
• Exact dynamics of concurrence-based entanglement in a system of four spin-1/2 particles on a triangular ladder structure
• Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition
• Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
• Quantum correlations in a cluster spin model with three-spin interactions
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Entanglement dynamics in minimal Kitaev chains
• Nonreciprocal flow of fluctuations, populations and correlations between doubly coupled bosonic modes