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

• URL: http://arxiv.org/abs/2309.15034v2
• Date: Mon, 19 Aug 2024 15:08:47 GMT
• Title: Measurement-induced phase transition in a single-body tight-binding model
• Authors: Tony Jin, David G. Martin,
• Abstract summary: We study the statistical properties of a single free quantum particle evolving coherently on a discrete lattice in $rm d$ spatial dimensions. Our numerical results indicate that the system undergoes a Measurement-induced Phase Transition (MiPT) for $rm d>1$ from a $textitdelocalized$ to a $textitlocalized$ phase.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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