Growth of entanglement entropy under local projective measurements

TL;DR

This paper studies how local projective measurements affect entanglement entropy growth in a one-dimensional fermionic system, revealing a transition from linear to logarithmic growth and a stable area-law phase in the thermodynamic limit.

Contribution

It demonstrates that measurements induce a qualitative change in entanglement growth and establishes the existence of a single area-law phase in the thermodynamic limit for finite measurement rates.

Findings

Measurement causes entanglement growth to change from linear to logarithmic.

In the thermodynamic limit, entanglement entropy follows an area-law for any finite measurement rate.

Analysis of fluctuations supports the stability of the area-law phase.

Abstract

Non-equilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce an abrupt change in the scaling-law of the bipartite entanglement entropy, thus suggesting the existence of different non-equilibrium regimes. However, our understanding of how these regimes appear and whether they survive in the thermodynamic limit is much less established. Here we investigate these questions on a one-dimensional quadratic fermionic model: this allows us to reach system sizes relevant in the thermodynamic sense. We show that local projective measurements induce a qualitative modification of the time-growth of the entanglement entropy which changes from linear to logarithmic. However, in the stationary regime, the logarithmic behavior of the entanglement entropy do not survive in the thermodynamic limit and, for any finite value of the measurement rate, we numerically show the existence of a single area-law phase for the entanglement entropy. Finally, exploiting the quasi-particle picture, we further support our results analysing the fluctuations of the stationary entanglement entropy and its scaling behavior.