Critical Properties of Weak Measurement Induced Phase Transitions in Random Quantum Circuits

Competition between entangling dynamics and wave function collapsing measurements in quantum many-body systems can induce a measurement induced phase transition (MIPT) between phases with distinct entanglement structure. MIPTs in random quantum circuits are described by non-unitary Conformal Field Theories (CFTs) with zero central charge. We study the properties of these CFTs in Haar random circuits subject to various measurement models by computing the Lyapunov exponents, central effective charge, and bulk critical exponents. Specifically, we compute these quantities in two models of weak measurements, a measuring device modeled as a continuous Gaussian probe and a softened version of the standard projective measurement, at various measurement strengths. The effect of weak measurements on the universality class of the MIPT will be discussed.