Measurement-induced phase transition in a classical, chaotic many-body system

TL;DR

This paper demonstrates that local projective measurements in a classical chaotic many-body system can induce a phase transition that halts information spreading, similar to quantum measurement-induced transitions, with the transition belonging to the directed percolation class.

Contribution

It introduces a classical analog of measurement-induced phase transitions, showing how local projections can freeze information dynamics in chaotic systems.

Findings

Local projections can induce a phase transition in classical chaos.

The transition shifts the butterfly velocity and halts information spreading.

The critical point belongs to the directed percolation universality class.

Abstract

Local measurements in quantum systems are projective operations which act to counteract the spread of quantum entanglement. Recent work has shown that local, random measurements applied to a generic volume-law entanglement generating many-body system are able to force a transition into an area-law phase. This work shows that projective operations can also force a similar classical phase transition; we show that local projections in a chaotic system can freeze information dynamics. In rough analogy with measurement-induced phase transitions, this is characterized by an absence of information spreading instead of entanglement entropy. We leverage a damage-spreading model of the classical transition to predict the butterfly velocity of the system both near to and away from the transition point. We map out the full phase diagram and show that the critical point is shifted by local projections, but remains in the directed percolation universality class. We discuss the implication for other classical chaotic many-body systems.