Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

TL;DR

This paper demonstrates a sharp phase transition in a many-body quantum system under measurement, revealing a measurement-induced transition from entangled to uncorrelated states, characterized by rare fluctuations and a non-Hermitian Hamiltonian approach.

Contribution

It introduces the concept of a measurement-induced phase transition in many-body systems, analyzed through a non-Hermitian Hamiltonian framework, supported by analytical and numerical results.

Findings

Identifies a sharp transition between entangled and Zeno states.

Shows the transition is encoded in rare fluctuations, not average dynamics.

Uses a non-Hermitian Quantum Ising model to capture the transition.

Abstract

It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.