Entanglement Scrambling in 2d Conformal Field Theory

TL;DR

The paper shows that entanglement scrambling in 1+1d CFTs after a global quench depends crucially on the spectrum of conserved currents. By analyzing boundary-state and thermal-double quenches through twist-field correlators and their light-cone singularities, it identifies a critical effective current central charge, $c_{\rm currents}$, separating current-dominated (quasiparticle-like) behavior from non-universal scrambling. In the large-$c$ (holographic) limit, gravity computations reproduce maximal scrambling with a suppressed, nonuniversal dip, and the D1–D5 CFT illustrates how stringy corrections modify memory. The work clarifies when the free quasiparticle picture applies and when holographic intuition dominates, providing a framework for understanding entanglement dynamics in diverse 2d CFTs.

Abstract

We investigate how entanglement spreads in time-dependent states of a 1+1 dimensional conformal field theory (CFT). The results depend qualitatively on the value of the central charge. In rational CFTs, which have central charge below a critical value, entanglement entropy behaves as if correlations were carried by free quasiparticles. This leads to long-term memory effects, such as spikes in the mutual information of widely separated regions at late times. When the central charge is above the critical value, the quasiparticle picture fails. Assuming no extended symmetry algebra, any theory with $c>1$ has diminished memory effects compared to the rational models. In holographic CFTs, with $c \gg 1$, these memory effects are eliminated altogether at strong coupling, but reappear after the scrambling time $t \gtrsim β\log c$ at weak coupling.

Figures (7)

• Figure 1: $(a)$ Quasiparticle picture for the entanglement entropy of two disjoint intervals. Entangled pairs are created at $t=0$, which propagate in opposite directions at the speed of light. When one of the particles enters $A$ and the other enters $B$, the entanglement entropy $S_{A\cup B}$ decreases. $(b)$ Memory effect in the entanglement entropy of two separated intervals after a global quantum quench. For intervals of size $L$ separated by a distance $D>L$, the dip is centered at $t = (D+L)/2$ and extends over the range $D/2 < t < D/2 + L$. The solid line is the free quasiparticle answer, and the dashed line is the holographic answer.
• Figure 2: Schematic illustration of the method of images. The conformal transformation properties of the correlator with insertions $w_{1,2,3,4}$ in the UHP are identical to those of the holomorphic 8-point function in the full plane, with image points $w_{i=5,6,7,8} = \bar{w}_{9-i}$. The solid red lines indicate the regions $A$ and $B$.
• Figure 3: Light cone limit $x \to 0$, $\bar{x} \to 1$.
• Figure 4: (a) Entanglement regions in the thermal double model, corresponding to $S_{A\cup B}$ in the original CFT. (b) Simplified setup, with an interval in the CFT and an offset interval in the thermal double. This setup exhibits the same features, including long-term memory effects in the quasiparticle picture that are not necessarily present in CFT.
• Figure 5: Quasiparticle picture for the offset-intervals entanglement in the thermal double model. (a) Entangled quasiparticle pairs (blue dots) in systems 1 and 2 are separated by $\Delta x \sim \beta$ at $t = 0$ (dashed horizontal line). Under time evolution, the particles move in opposite directions. Eventually both particles enter region $A'$. (b) Quasiparticle prediction for the entanglement entropy $S_{A'}-2S_0$ of region $A'$. When the entangled pair enters region $A'$, the entanglement entropy decreases.