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

TL;DR

This paper investigates how continuous measurements affect a quantum particle on a lattice, revealing a phase transition from delocalized to localized states as measurement strength increases, supported by numerical and RG analyses.

Contribution

It introduces the concept of measurement-induced phase transition in a single-particle model and combines numerical simulations with perturbative RG to analyze the transition.

Findings

System undergoes a transition from delocalized to localized phase at critical measurement strength

Delocalized phase corresponds to smooth surface growth, localized to rough surface growth

RG computations qualitatively agree with numerical results at one-loop order

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.