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.
Highlights
No scrambling time (b) result is fixed universally by conformal symmetry, and depends only on the central charge c of the conformal field theory (CFT)
We investigate how entanglement spreads in time-dependent states of a 1+1 dimensional conformal field theory (CFT)
In rational CFTs, which have central charge below a critical value, entanglement entropy behaves as if correlations were carried by free quasiparticles
Summary
No scrambling time (b) result is fixed universally by conformal symmetry, and depends only on the central charge c of the CFT. In a theory of free quasiparticles, the entanglement entropy SA∪B(t) is shown in figure 1b After the quench, it grows linearly as entangled pairs spread, and saturates at the thermal value for temperature β ∼ ξ. At the midpoint of the dip, the left-moving quasiparticles in region A are maximally entangled with the right-moving quasiparticles in region B, so SA∪B is exactly half the thermal value (after subtracting the divergent contribution at t = 0) In this scenario, maximally entangled degrees of freedom remain maximally entangled even as they propagate to very large separation. It was claimed in [15, 17] that the free quasiparticle behavior for multi-interval entanglement after a global quench is universal to all conformal field theories. Our aim is to reconcile these two pictures, and to understand the middle ground
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