Global entanglement in a topological quantum phase transition

Abstract

A useful approach to characterize and identify quantum phase transitions lies in the concept of multipartite entanglement. In this paper, we consider well-known measures of multipartite (global) entanglement, i.e., average linear entropy of one-qubit and two-qubit reduced density matrices, in order to study topological quantum phase transition (TQPT) in the Kitaev Toric code Hamiltonian with a nonlinear perturbation. We provide an $exact$ mapping from aforementioned measures in the above model to internal energy and energy-energy correlations in the classical Ising model. Accordingly, we find that the global entanglement shows a continuous and sharp transition from a maximum value in the topological phase to zero in the magnetized phase in a sense that its first-order derivative diverges at the transition point. In this regard, we conclude that not only can the global entanglement serve as a reasonable tool to probe quantum criticality at TQPTs, but it also can reveal the highly entangled nature of topological phases. Furthermore, we also introduce a conditional version of global entanglement which becomes maximum at the critical point. Therefore, regarding a general expectation that multipartite entanglement reaches maximum value at the critical point of quantum many-body systems, our result proposes that the conditional global entanglement can be a good measure of multipartite entanglement in TQPTs.

9 pages, 4 figures

References in corpus (19)

• Identifying Topological Order by Entanglement Entropy
• Robustness of a perturbed topological phase
• Multipartite entanglement in topological quantum phases
• A quantum topological phase transition at the microscopic level
• Adiabatic Preparation of Topological Order
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Fidelity analysis of topological quantum phase transitions
• Operational Classification and Quantification of Multipartite Entangled States
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
• Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Dynamics of Global Entanglement under Decoherence
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• On the robustness of topological quantum codes: Ising perturbation
• Phase transition in a noisy Kitaev toric code model