Infinite-randomness criticality in monitored quantum dynamics with static disorder

Understand

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates.

• These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate.
• In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size $\ell$ scales as $S \sim \sqrt{\ell}$; moreover, the dynamical critical exponent $z = \infty$.
• The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents.