Entanglement transition in a monitored free fermion chain -- from extended criticality to area law

TL;DR

This paper investigates how continuous monitoring affects entanglement in a free fermion chain, revealing a transition from a critical phase with subextensive entanglement to an area-law phase, driven by measurement strength.

Contribution

It uncovers an unconventional entanglement transition in a realistic free fermion model under continuous measurement, highlighting the role of measurement in phase transition dynamics.

Findings

Weak monitoring leads to subextensive entanglement growth with critical behavior.

Strong monitoring induces a transition to an area-law entanglement regime.

Finite size corrections suggest a Berezinskii-Kosterlitz-Thouless transition mechanism.

Abstract

We analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.