Fate of the area-law after partial measurement in quantum field theories

Understand

We calculate numerically the R\'enyi bipartite entanglement entropy of the ground state of Klein-Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators in $d=1,2$ and $3$ dimensions.

• We show that after partial measurement as far as the two parts are connected the area-law is valid in generic dimensions except in $d=1$ conformal field theories.
• When due to the measured region the two parts are disconnected, the entanglement entropy decreases exponentially with respect to the minimum distance between the regions.
• In the massless case the decay is power-law with a universal dimension-dependent exponent.