Alioscia Hamma, Lukasz Cincio, Siddhartha Santra, Paolo Zanardi, Luigi Amico
We study the behaviour of the Renyi entropies for the toric code subject to a variety of different perturbations, by means of 2D DMRG and analytical methods. We find that Renyi entropies of different index $\alpha$ display derivatives with opposite sign. This splitting happens at a low value of $\alpha$, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, and cluster states. The fact that the size of the subsystem does not need to scale with the correlation length, makes it possible for this effect to be accessed experimentally.
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http://arxiv.org/abs/1211.4538
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