Measurement-induced phase transition in a single-body tight-binding model

Abstract

We study the statistical properties of a single free quantum particle evolving coherently on a discrete lattice in $\mathrm{d}$ 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 $\mathrm{d}>1$ from a $\text{delocalized}$ to a $\text{localized}$ phase as the measurement strength ${\hat{I}}^3$ is increased beyond a critical value ${\hat{I}}_c^3$. In the language of surface growth, the delocalized phase corresponds to a $\text{smooth}$ phase while the localized phase corresponds to a $\text{rough}$ phase. We support our numerical results with perturbative renormalization group (RG) computations which are in qualitative agreement at one-loop order.

5 pages, 5 figures, 1 table + Supplemental Material