Evolution of Entanglement Entropy in Orbifold CFTs

TL;DR

The paper investigates how Renyi entanglement entropy evolves after local twist-operator excitations in cyclic and symmetric orbifold CFTs built from two compact bosons. Using the replica method and detailed four-point functions, it shows that rational radius (η) yields a universal late-time constant determined by the twist's quantum dimension, while irrational η in the cyclic case produces a novel log-log time growth, indicating a new integrable yet irrational CFT class. For symmetric orbifolds, the late-time growth acquires an additional factorial term reflecting projection differences. Recasting the findings in terms of light-like mutual information further highlights distinct information-theoretic behavior across rational and irrational regimes, suggesting broad implications for entanglement dynamics and OTOCs 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.

Figures (7)

• Figure 1: The setup of the 2nd Renyi entanglement entropy $\Delta S^{(2)}_A$ for a half line $A$
• Figure 2: The plot of the function $F_2(x,1-x)$ for $\eta={10\over 11}$ as a function of $\delta={\pi\over -\log x}$. The left figure for $0\leq \delta\leq 0.02$. The right one for $0\leq \delta\leq 1.5$.
• Figure 3: The plot of the function $F_2(x,1-x)$ for $\eta=\sqrt{2}$ as a function of $\delta={\pi\over -\log x}$. The left figure for $0\leq \delta\leq 1.6$. The right one for $0\leq \delta\leq 0.06$. The blue thick curves describe the plots. The black ones are the numerical fits.
• Figure 4: The plot of the ratio $F_2(x,1-x)/\delta$ for $\eta=\sqrt{2}$ as a function of $\delta={\pi\over -\log x}$. We took $0\leq \delta\leq 0.05$.
• Figure 5: The plot of the function $F_3(x,1-x)$ for $\eta=\sqrt{2}$ as a function of $\delta={\pi\over -\log x}$. The left figure for $0\leq \delta\leq 1.6$. The right one for $0\leq \delta\leq 0.05$. The actual numerical plots are blue colored.