Entanglement in a fermion chain under continuous monitoring

TL;DR

This paper investigates how continuous local measurements affect entanglement in a free fermion chain, developing a theory based on generalized hydrodynamics and validating it with numerical simulations.

Contribution

It introduces a simple theoretical framework for entanglement evolution under monitoring in integrable systems, supported by extensive numerical validation.

Findings

Weak measurements destroy volume law entanglement.

The proposed theory accurately predicts entanglement dynamics.

Entanglement entropy evolution matches numerical results.

Abstract

We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.