We study the behavior of the Renyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that Renyi entropies of different index alpha display derivatives with opposite sign, 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, cluster states, and other quantum spin liquids. 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.
Local Response of Topological Order to an External Perturbation
Amico Luigi
2013
Abstract
We study the behavior of the Renyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that Renyi entropies of different index alpha display derivatives with opposite sign, 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, cluster states, and other quantum spin liquids. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
