Measurement-induced phase transition for free fermions above one dimension

TL;DR

This paper develops a theoretical framework for measurement-induced phase transitions in free fermion systems in higher dimensions, identifying critical behavior and confirming findings with numerical simulations.

Contribution

It introduces a field-theoretic approach for free fermions in dimensions greater than one, deriving critical indices and analyzing the phase transition using renormalization-group techniques.

Findings

Identifies a phase transition characterized by different entanglement scaling laws.

Calculates critical indices using one-loop renormalization-group analysis.

Numerically estimates the correlation length exponent as approximately 1.4 in 2D.

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, $\nu \approx 1.4$.