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arXiv · 2309.15034

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

Tony Jin·David G. Martin
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Abstract

We study the statistical properties of a single free quantum particle evolving coherently on a discrete lattice in ${\rm d}$ 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 ${\rm d}>1$ from a $\textit{delocalized}$ to a $\textit{localized}$ 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 $\textit{smooth}$ phase while the localized phase corresponds to a $\textit{rough}$ 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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Tony Jin, David G. Martin. 2023-09-26. Measurement-induced phase transition in a single-body tight-binding model. https://doi.org/10.1103/physrevb.110.l060202

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