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.

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.

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.

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.