Global entanglement in a topological quantum phase transition

TL;DR

This paper demonstrates that global entanglement measures can effectively identify and characterize topological quantum phase transitions in the Kitaev Toric code model, revealing critical behavior and entanglement properties.

Contribution

It introduces an exact mapping of global entanglement measures to classical Ising model quantities and proposes conditional global entanglement as a new indicator for TQPTs.

Findings

Global entanglement sharply transitions at the TQPT

First derivative of entanglement diverges at critical point

Conditional global entanglement peaks at the 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.