We study the statistical properties of a single free quantum particle evolving coherently on a discrete lattice in $\mathit{\text{d}}$ spatial dimensions where every lattice site is additionally subject to continuous measurement of the occupation number. Our numerical results indicate that the system undergoes a measurement-induced phase transition (MiPT) for $\mathit{\text{d}}>1$ from a delocalized to a localized phase as the measurement strength $\gamma$ is increased beyond a critical value ${\gamma }_c$. In the language of surface growth, the delocalized phase corresponds to a smooth phase while the localized phase corresponds to a rough phase. We support our numerical results with perturbative renormalization group (RG) computations which are in qualitative agreement at one-loop order.

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• Noise-induced transitions
• Nonequilibrium statistical mechanics
• Open quantum systems & decoherence
• Quantum information theory
• Quantum measurements
• Quantum stochastic processes
• Kardar–Parisi–Zhang equation
• Lindblad equation
• Path-integral methods
• Stochastic differential equations