Critical correlations and entanglement in the measured quantum Ising model

While the low-energy properties of one-dimensional quantum critical states are well understood, it is an ongoing problem to determine how they respond to local measurements, which can have highly non-local effects due to the underlying power-law correlations. To approach this question, we analytically and numerically investigate the effect of performing an extensive number of local measurements on the ground state of the critical quantum Ising model. Using exact free fermion numerics and analytical field-theoretic arguments, we show that parity-preserving local measurements do not modify the long-distance behavior of measurement-averaged physical quantities. In contrast, we identify a particular class of post-measurement quantum states whose correlations are dramatically altered: the exponents governing power-law correlations and the effective central charge appearing in the entanglement entropy are shown to vary continuously with the measurement rate. This work reveals the kinds of quantum critical correlations which survive measurement, and further develops a theoretical framework that can be applied to a wide class of measured quantum systems.