Spacetime duality between localization transitions and measurement-induced transitions

Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via spatial disorder, or subjecting the system to nonunitary evolution, e.g., via projective measurements. Here we employ the idea of spacetime rotation of a circuit to explore the relation between systems that fall into these two classes. In particular, by spacetime rotating unitary Floquet circuits that display a localization transition, we construct nonunitary circuits that display a rich variety of entanglement scaling and phase transitions. One outcome of our approach is a nonunitary circuit for free fermions in one dimension that exhibits an entanglement transition from logarithmic scaling to volume-law scaling. This transition is accompanied by a "purification transition" analogous to that seen in hybrid projective-unitary circuits. We follow a similar strategy to construct a nonunitary two-dimensional (2D) Clifford circuit that shows a transition from area to volume-law entanglement scaling. Similarly, we spacetime rotate a 1D spin chain that hosts many-body localization to obtain a nonunitary circuit that exhibits an entanglement transition. Finally, we introduce an unconventional correlator and argue that if a unitary circuit hosts a many-body localization transition then the correlator is expected to be singular in its nonunitary counterpart as well.