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  • 1.
    Caputa, P.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rams, M. M.
    Quantum dimensions from local operator excitations in the Ising model2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 5, article id 055002Article in journal (Refereed)
    Abstract [en]

    We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics. © 2017 IOP Publishing Ltd.

  • 2.
    Caputa, Pawel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden; Kyoto University, Japan.
    Kusuki, Yuya
    Takayanagi, Tadashi
    Watanabe, Kento
    Evolution of entanglement entropy in orbifold CFTs2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 24, article id 244001Article in journal (Refereed)
    Abstract [en]

    In this work we study the time evolution of the Renyi entanglement entropy for locally excited states created by twist operators in the cyclic orbifold (T-2)(n)/Z(n) and the symmetric orbifold (T-2)(n)/S-n. We find that when the square of its compactification radius is rational, the second Renyi entropy approaches a universal constant equal to the logarithm of the quantum dimension of the twist operator. On the other hand, in the non-rational case, we find a new scaling law for the Renyi entropies given by the double logarithm of time log log t for the cyclic orbifold CFT.

  • 3.
    Caputa, Pawel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm univ.
    Simon, Joan
    Stikonas, Andrius
    Takayanagi, Tadashi
    Watanabe, Kento
    Scrambling time from local perturbations of the eternal BTZ black hole2015In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, article id 011Article in journal (Refereed)
    Abstract [en]

    We compute the mutual information between finite intervals in two noncompact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time t(omega) in the large c limit. We determine the time scale, called the scrambling time, at which the mutual information vanishes and the original entanglement between the thermofield double gets destroyed by the perturbation. We provide a holographic description in terms of a free falling particle in the eternal BTZ black hole that exactly matches our CFT calculations. Our results hold for any time tw. In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.

  • 4.
    Caputa, Pawel
    et al.
    KTH. Stockholm Univ, Sweden.
    Veliz-Osorio, Alvaro
    Entanglement constant for conformal families2015In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 92, no 6, article id 065010Article in journal (Refereed)
    Abstract [en]

    We show that in 1 + 1 dimensional conformal field theories, exciting a state with a local operator increases the Renyi entanglement entropies by a constant which is the same for every member of the conformal family. Hence, it is an intrinsic parameter that characterizes local operators from the perspective of quantum entanglement. In rational conformal field theories this constant corresponds to the logarithm of the quantum dimension of the primary operator. We provide several detailed examples for the second Renyi entropies and a general derivation.

  • 5.
    Caputa, Pawet
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Kyoto University, Kyoto, Japan .
    Simon, Joan
    Stikonas, Andrius
    Takayanagi, Tadashi
    Quantum entanglement of localized excited states at finite temperature2015In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 1Article in journal (Refereed)
    Abstract [en]

    In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.

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