Entanglement harvesting in conformal field theory

TL;DR

This work extends entanglement harvesting to general $d$-dimensional conformal field theories by coupling two Unruh–DeWitt detectors to scalar primary operators with scaling dimension $\Delta$. Using a perturbative Dyson expansion, the authors derive a reduced two-detector density matrix governed by conformally fixed two-point functions, show that increasing $\Delta$ suppresses negativity and mutual information, and provide asymptotic closed-form results. In holographic CFTs, AdS/CFT enables a clean separation between field-sourced entanglement and field-mediated communication, allowing a diagnostic of genuine harvesting versus communication-induced correlations. The results illuminate how operator dimension shapes operational access to field entanglement and offer practical approximations that align with numerical data, with implications for probing entanglement structure in interacting quantum fields and holographic duals.

Abstract

We study entanglement harvesting in general $d$-dimensional conformal field theories using pointlike Unruh-DeWitt detectors coupled to scalar primary operators. This extends standard harvesting protocols beyond free fields to interacting conformal theories and arbitrary spatial dimensions. We find that increasing the operator scaling dimension suppresses both negativity and mutual information, reflecting the faster decay of correlations. For holographic CFTs, we show that bulk effective field theory enables a separation between field-harvested and communication-mediated entanglement. We also derive asymptotic, closed-form approximations that agree well with numerical results.

Figures (17)

• Figure 1: We consider two pointlike detectors with Gaussian switching functions with width $T$. The detectors are spatially separated by a distance $L$, and the temporal centres of the Gaussian switching functions are separated by $\delta$. At some separation $L\sim 10T$, the communication contribution from the Gaussian tails is negligible and the detectors can be taken to be effectively spacelike-separated. When $\delta = L$, the centre of one detector lies along the lightcone of the centre of the other.
• Figure 2: Here we plot the self-excitation probability (local noise term) $\mathcal{L}_{\textsc{a}\textsc{a}}$ given in eq. \ref{['eq:Lii']} as a function of the scaling dimension $\Delta$, using $T\Omega = 10$. The red dashed line shows the leading-order term in $1/(T \Omega)$, given in eq. \ref{['eq:largeOmega0']}. Since the subleading terms in this expansion scale with $\Delta$, we expect larger deviations of the first-order fit for larger $\Delta$.
• Figure 3: The above plots show $|\mathcal{L}_\textsc{ab}| / \overline{\lambda}^2$, used in the calculation of the mutual information, obtained via numerical analysis of eq. \ref{['eq:Lij']}. On the left side, $L/T$ and $\Delta$ are varied, and we have set $\delta/T = 0$. In this case, $\mathcal{L}_{\textsc{a}\textsc{b}}$ is real. On the right side, $\delta/T$ and $\Delta$ are varied, and we have set $L/T = 10$. For $\delta/T \neq 0$, $\mathcal{L}_{\textsc{a}\textsc{b}}$ is generally complex. For both plots, we use $\Omega T = 10$. The colour band widths are approximately equal for a fixed $L/T$ or $\delta/T$, indicating that $|\mathcal{L}_\textsc{ab}|$ decays roughly exponentially with the operator dimension $\Delta$ for our choices of parameters. In figure \ref{['fig:Lab_L_and_delta_slices']} of appendix \ref{['appx:leadingObehaviour']} we show cross-sections of these plots to compare the numerical results to the asymptotic behaviour given in eq. \ref{['eq:Lij_leading_order']}.
• Figure 4: The above plots show $|\mathcal{M}| / \overline{\lambda}^2$, used in the calculation of negativity, obtained via numerical analysis of eq. \ref{['eq:M_numerical']}. On the left side, $L/T$ and $\Delta$ are varied, and we have set $\delta/T = 0$. On the right side, $\delta/T$ and $\Delta$ are varied, and we have set $L/T = 10$. For both plots, we use $\Omega T = 10$. In the right plot, for a fixed $\delta/T$, the colour band widths are approximately equal, indicating that $|\mathcal{M}|$ decays roughly exponentially with $\Delta$ in this regime. The same can be said in the left plot for a fixed $L/T \gtrsim 1$. For $L/T \lesssim 1$, we see $|\mathcal{M}|$ increases with $\Delta$. In figure \ref{['fig:M_L_and_delta_slices']} of appendix \ref{['appx:leadingObehaviour']} we show cross-sections of these plots to compare our numerical results to the asymptotic behaviour given in eq. \ref{['eq:M_leading_order']}.
• Figure 5: These plots show the negativity between the two detectors as defined in eq. \ref{['eq:negativity2']}. On the left side, $L/T$ and $\Delta$ are varied, and we have set $\delta/T = 0$. The solid black line marks the maximum $\mathcal{N}$ for a given $L/T$ as given by the approximation in eq. \ref{['eq:max_Delta']}. In the right panel, we set $L/T = 10$ and vary $\delta/T$. Here we see the negativity clearly maximised when the detectors are in light contact. In both plots, we have set $\Omega T = 10$. The gray dashed lines in each figure show an approximation of the boundary where the negativity vanishes, obtained in closed form in eqs. \ref{['eq:nomore']} and \ref{['eq:nomore2']} for the left and right figures respectively. In figure \ref{['fig:Negativity_L_and_delta_slices']} of appendix \ref{['appx:leadingObehaviour']} we show cross-sections of these plots to compare our numerical results to the asymptotic behaviour given in eq. \ref{['eq:hullabaloo']}, as well as higher-order and near-lightcone approximations.