Measurement-induced criticality in quasiperiodic modulated random hybrid circuits

The measurement-induced phase transition (MIPT) is an out-of-equilibrium phase transition separating entangling and disentangling quantum dynamics in hybrid quantum circuits, resulting from the competition between random unitary dynamics and local projective measurements. In this work, we study the stability of the MIPT in one dimension to quenched quasiperiodic (QP) modulations as captured in the context of equilibrium statistical mechanics by the Luck bound ν≥1/(1−β), for the correlation length exponent ν. Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent β to exceed the Luck bound and destabilize the MIPT. Through extensive numerical simulations of random Clifford circuits, we establish an RG-flow to a series of infinite-QP phase transitions and characterize the corresponding universal properties. In particular, we find a stretched exponential space-time scaling behavior with an activation exponent ψ=β and a correlation length exponent that saturates the Luck bound. Our findings agree with recent analytic mapping of the MIPT to ground state properties of the quantum Potts model in the replica limit.