Würzburg Seminar on Quantum Field Theory and Gravity

Weak measurements can be viewed as a soft projection that interpolates between an identity operator and a projection operator, and can induce an effective central charge distinct from the unmeasured CFT. In the first part, I will discuss the effect of measurement and postselection on the critical ground state of a Luttinger liquid theory. Depending on the Luttinger parameter K, the effect of measurement is irrelevant, marginal, or relevant, respectively. When the measurement is marginal, and we find a critical state whose entanglement entropy exhibits a logarithmic behavior with a continuous effective central charge as a function of measurement strength.
Inspired by this result, in the second part, I will discuss a holographic description of the weak measurement. The weak measurement is modeled by an interface brane, separating different geometries dual to the post-measurement state and the unmeasured CFT. In an infinite system, the weak measurement is related to ICFT via a spacetime rotation. We find that the holographic entanglement entropy with twist operators located on the defect is consistent in both calculations for ICFT and weak measurements. In a finite system, the weak measurement can lead to a rich phase diagram, in which the post-measurement geometry can realize a Python’s lunch.