Effect of measurements on the entanglement entropy of critical ground states in 1+1d

Measurement provides a powerful tool to manipulate quantum information in a quantum many-body system. In particular, it has been shown that measurements on particular quantum states can help carry out quantum computations and prepare new quantum states with long-range entanglement. For this work, we focus on the effect of measurements on the entanglement within the ground states of various one-dimensional critical systems. Before measurements, such a critical ground state can be viewed as the ground state of a 1+1d conformal field theory (CFT), whose entanglement entropy (EE) is known to scale as the logarithm of the subsystem size $L$ with the prefactor proportional to the central charge $c$. After measurements, we demonstrate that when the measurement leads to a relevant perturbation, the EE is reduced from the logarithmic scaling to an area law even if the correlation functions on the post-measurement state still follow a power law, suggesting a diverging correlation length. More interestingly, when the perturbation induced by the measurement is exactly marginal, the EE retains the logarithmic scaling $S_A = frac{c_ ext{eff}}{3} log(L)$ but with a continuously tunable effective central charge $0