Monte Carlo matrix-product-state approach to the false vacuum decay in the monitored quantum Ising chain

TL;DR

This paper investigates how continuous measurements influence false vacuum decay in a monitored quantum Ising chain, revealing accelerated decay, thermalization, and quantum Zeno effects through advanced numerical simulations.

Contribution

It introduces a novel Monte Carlo matrix-product-state method combining stochastic trajectories to study measurement effects on quantum phase decay.

Findings

Measurements accelerate initial decay of the false vacuum.

At long times, the system thermalizes to an infinite-temperature state.

Large measurement rates induce a quantum Zeno regime.

Abstract

In this work we characterize the false vacuum decay in the ferromagnetic quantum Ising chain with a weak longitudinal field subject to continuous monitoring of the local magnetization. Initializing the system in a metastable state, the false vacuum, we study the competition between coherent dynamics, which tends to create resonant bubbles of the true vacuum, and measurements which induce heating and reduce the amount of quantum correlations. To this end we exploit a numerical approach based on the combination of matrix product states with stochastic quantum trajectories which allows for the simulation of the trajectory-resolved non-equilibrium dynamics of interacting many-body systems in the presence of continuous measurements. We show how the presence of measurements affects the false vacuum decay: at short times the departure from the local minimum is accelerated while at long times the system thermalizes to an infinite-temperature incoherent mixture. For large measurement rates the system enters a quantum Zeno regime. The false vacuum decay and the thermalization physics are characterized in terms of the magnetization, connected correlation function, and the trajectory-resolved entanglement entropy.