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arXiv · 2309.12405

Measurement-induced phase transition for free fermions above one dimension

Igor Poboiko·Igor V. Gornyi·Alexander D. Mirlin
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Abstract

A theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. The critical point separates a gapless phase with $\ell^{d-1} \ln \ell$ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with $\ell^{d-1}$ scaling, where $\ell$ is a size of the subsystem. The problem is mapped onto an SU($R$) replica non-linear sigma model in $d+1$ dimensions, with $R\to 1$. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for $d = 1+ \epsilon$ with $\epsilon \ll 1$. Further, we carry out a numerical study of the transition for a $d=2$ model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, $\nu \approx 1.4$.

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Igor Poboiko, Igor V. Gornyi, Alexander D. Mirlin. 2023-09-21. Measurement-induced phase transition for free fermions above one dimension. https://doi.org/10.1103/physrevlett.132.110403

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