1306.4990 (Claudio Castelnovo)

Negativity and topological order in the toric code    [PDF]

Claudio Castelnovo

In this manuscript we study the behaviour of the entanglement measure dubbed negativity in the context of the toric code model. Using a method introduced recently by Calabrese, Cardy and Tonni [Phys. Rev. Lett. 109, 130502 (2012)], we are able to obtain an exact expression which illustrates how the non-local correlations present in a topologically ordered state reflect in the behaviour of the negativity of the system. The negativity is non-vanishing only if the partitions are topologically non-trivial, which is consistent with the fact that topologically trivial disconnected subsystems are separable in a topologically ordered state. With this calculation we also show that the negativity captures only the off-diagonal (`quantum') contribution to the topological entropy and it is insensitive to the diagonal part. Indeed, we find that the negativity vanishes for the classical topologically ordered 8-vertex model, which on the contrary exhibits a finite topological contribution in the von Neumann entropy.

View original: http://arxiv.org/abs/1306.4990