Measurments-induced quantum phase transitions

TL;DR

This paper investigates how local projective measurements induce a quantum phase transition in a 1D fermionic system, changing entanglement growth from linear to logarithmic and revealing a single area-law phase in the thermodynamic limit.

Contribution

It demonstrates that measurements qualitatively alter entanglement dynamics and identifies a measurement-induced phase transition with a stable area-law phase.

Findings

Entanglement growth changes from linear to logarithmic due to measurements.

In the thermodynamic limit, a single area-law phase persists for finite measurement rates.

Analytical arguments support the numerical results.

Abstract

Dynamical phase transitions induced by local projective measurements have attracted a lot of attention in the past few years. It has been in particular argued that measurements may induce an abrupt change in the scaling law of the bipartite entanglement entropy. In this work we show that local projective measurements on a one-dimensional quadratic fermionic system induce a qualitative modification of the time growth of the entanglement entropy, changing from linear to logarithmic. However, in the stationary regime, the logarithmic behavior of the entanglement entropy does 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. We give analytical arguments supporting our conclusions.