Universal corrections to entanglement entropy of local quantum quenches

TL;DR

This work analyzes finite-width local quenches in 1+1d CFTs at finite temperature, showing that the first nontrivial width correction to single-interval Rényi and entanglement entropies at ${\cal O}(ε^2)$ is universal and controlled by the stress tensor on the replica geometry, with an overall factor set by the quench dimension $Δ_O$. The authors derive this universal correction using both conformal block and OPE arguments, verify it against exact results in minimal models and the free fermion theory, and confirm holographic equivalence via backreacted BTZ geometries. They extend the framework to CFTs with higher-spin symmetry by introducing a small spin-3 chemical potential $μ$, showing an ${\cal O}(ε^2 μ^2)$ universal time dependence tied to $\langle T W W\rangle_n$, and provide explicit spin-3 results and checks against ${\cal W}_{1+\infty}$/free-fermion theories. Overall, the paper demonstrates that local quenches imprint universal, theory-independent entanglement dynamics in a broad class of 2d CFTs, with clear holographic and higher-spin extensions and implications for quantum quenches in strongly coupled systems.

Abstract

We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width, ε. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order ε^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ε^2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ε^2 correction to the entanglement entropy for small μ, and show that the contribution at order μ^2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

Figures (9)

• Figure 1: Left: A finite width pulse generated by a local quench propagates along the lightcone and reaches the interval $A$ after time $t=l_1$. Right: Typical profile for the time evolution of the change in the (second) Rényi entropy after the quench, for a minimal model CFT. Following an initial spike or overshoot after (before) the pulse enters (exits) the interval, $\Delta S_A^{(n)}$ settles toward a constant value and subsequently vanishes when the pulse exits the interval.
• Figure 2: A lump of energy density of width $\sim \epsilon =0.1$ and height normalized to unity at $t=0$ splits into left- and right-moving pulses moving along the light-cone, shown centred at $x=\pm0.5$ at $t=0.5$.
• Figure 3: A strip of width $\beta$ on the $x$-plane, representing the thermal cylinder ${\mathbb R}\times S^{1}_\beta$. The operators ${ {\cal O}^\dagger}$ and ${\cal O}$ are inserted at $x_4$ and $x_1$ respectively. The end-points of the interval $A$ are at $x_2$ and $x_3$ whose values are given by (Lorentzian) lightcone coordinates at any given real time $t$.
• Figure 4: The uniformization map takes the branched $n$-sheeted cover of the cylinder to the $w$-plane. Each sheet maps to a wedge with opening angle $2\pi/n$. Shown are the locations of pairs of operator insertions in the fundamental wedge, $w_1\equiv w(x_1^{(1)})$ and $w_4\equiv w(x_4^{(1)})$, and their images. The relative locations of the operator insertions/excitations as a function of time are indicated in blue, in the fundamental domain.
• Figure 5: Time dependence of the second Rényi entropy for the minimal model quench, with ${p}/{p'} = 1.21$, $\beta=1, l_1=1, l_2=1.2$ and $\epsilon=0.005$. Shown above are the exact result (blue curve), the step jump at order $\epsilon^0$ (dashed black), and the approximation at order $\epsilon^2$ (in red).