Scaling of quantum Zeno dynamics in thermodynamic systems

TL;DR

This paper investigates how the quantum Zeno effect manifests in large many-body systems, specifically the Ising and LMG models, revealing measurement frequency requirements for observing QZE.

Contribution

It provides a detailed analysis of the conditions under which quantum Zeno dynamics can be observed in thermodynamic many-body systems, highlighting differences across phases.

Findings

QZE requires measurement frequency comparable to system size in the Ising model

QZE observed in the symmetry broken phase of LMG model under similar conditions

QZE is easily observed in the polarized phase of the LMG model

Abstract

We study the quantum Zeno effect (QZE) in two many-body systems, namely the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick (LMG) model, coupled to a central qubit. Our result shows that in order to observe QZE in the Ising model, the frequency of the projective measurement should be of comparable order to that of the system sizes. The same criterion also holds in the symmetry broken phase of the LMG model while in the model's polarized phase, the QZE can be easily observed.