Entanglement Scrambling in 2d Conformal Field Theory

TL;DR

This paper explores how entanglement spreads in 1+1 dimensional conformal field theories, revealing different behaviors depending on the central charge and coupling strength, with implications for memory effects and scrambling.

Contribution

It provides a detailed analysis of entanglement dynamics in CFTs, highlighting the role of central charge and coupling in the quasiparticle picture and memory effects.

Findings

Rational CFTs exhibit long-term memory effects in entanglement.

Above a critical central charge, the quasiparticle picture breaks down.

In holographic CFTs, memory effects are suppressed at strong coupling but reappear after the scrambling time.

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 $t \gtrsim \beta \log c$ at weak coupling.