Scattering effect on entanglement propagation in RCFTs

TL;DR

This work analyzes how scattering between local excitations in 2D RCFTs affects entanglement propagation using the replica method. It shows that in RCFTs the entanglement is conserved after scattering, with Renyi entropies determined solely by the sum of the operators' quantum dimensions, tied to the finite fusion data. The results support a free-quasiparticle picture for entanglement spreading in integrable theories and contrast with chaotic holographic CFTs where scrambling occurs. The Ising CFT example illustrates the additive nature of entanglement contributions, and the general RCFT framework extends to arbitrary numbers of operators, highlighting the central role of quantum dimensions and fusion in entanglement dynamics.

Abstract

In this paper we discuss the scattering effect on entanglement propagation in RCFTs. In our setup, we consider the time evolution of excited states created by the insertion of many local operators. Our results show that because of the finiteness of quantum dimension, entanglement is not changed after the scattering in RCFTs. In this mean, entanglement is conserved after the scattering event in RCFTs, which reflects the integrability of the system. Our results are also consistent with the free quasiparticle picture after the global quenches.

Figures (17)

• Figure 1: The schematic picture of scattering of EPR pairs. The scattering is represented the red star, which corresponds to the unitary matrix $U$ on the Hilbelt space of particle $1$ and $3$.
• Figure 2: The figure of the setup we consider in this paper. $\mathcal{O}_a$ and $\mathcal{O}_b$ are primary operators. The index of operators means the sector of each primary operator. At $t=0$, these operators are inserted apart from the entangling surface (in this case actually a point) and entangling quasiparticles are emitted. $l_a$ and $l_b$ represent the length from entangling surface. We consider the case that A is given by the half of space $\{x \in \mathbb{R}|x>0 \}$.
• Figure 3:
• Figure 4: Configuration of the holomorphic part coordinates of operators on $z$ plane in the $n=4$ case. The blue dots represent the holomorphic coordinate of the local operators. Brown lines are the orbit of coordinates along the time evolution.
• Figure 5: The left picture represents the fusion transformation of the 4-point conformal block . The bold connecting two operators shows that we take the OPE of these operators. The thin lines shows the intermediate Identity sector. The right picture shows the sequence of fusion transformations to get the Rényi entropy $\Delta S_A^{(n)}$, which is a combination of fusion transformations in 4-point formal blocks.