Evolution of Entanglement Entropy in Orbifold CFTs

Abstract

In this work we study the time evolution of Renyi entanglement entropy for locally excited states created by twist operators in cyclic orbifold $(T^2{)}^n/{\mathbb{Z}}_n$ and 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.

28 pages, 7 figures. Invited contribution to the special issue of J. Phys. A: "John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday". v2: typos corrected, refs added, sec.5 improved. v3: affiliation, ref updated

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