Measurement induced criticality in quasiperiodic modulated random hybrid circuits
Gal Shkolnik, Aidan Zabalo, Romain Vasseur, David A. Huse, J. H. Pixley, Snir Gazit
Abstract
We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\ensuremath{\beta}$ to exceed the Luck bound $\ensuremath{\nu}\ensuremath{\ge}1/(1\ensuremath{-}\ensuremath{\beta})$ for the stability of the MIPT, where $\ensuremath{\nu}=1.28(2)$. Via robust numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent $\ensuremath{\beta}$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\ensuremath{\psi}\ensuremath{\cong}\ensuremath{\beta}$, finding excellent agreement with the conclusions of real-space renormalization group calculations.