Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles

TL;DR

This paper develops a phenomenological theory describing how entanglement evolves in monitored quantum many-body systems by modeling non-Hermitian quasiparticles that are stochastically reset by measurements, predicting various entanglement phases and transitions.

Contribution

It introduces a novel framework linking quasiparticle decay spectra to entanglement scaling and phase transitions in monitored quantum systems.

Findings

Predicts a critical phase with logarithmic entanglement scaling.

Identifies an area law phase and a continuous transition between phases.

Shows excellent agreement with numerical simulations on a quantum Ising chain.

Abstract

We put forward a phenomenological theory for entanglement dynamics in monitored quantum many-body systems with well-defined quasiparticles. Within this theory entanglement is carried by ballistically propagating non-Hermitian quasiparticles which are stochastically reset by the measurement protocol with rate given by their finite inverse lifetime. We write down a renewal equation for the statistics of the entanglement entropy and show that depending on the spectrum of quasiparticle decay rates different entanglement scaling can arise and even sharp entanglement phase transitions. When applied to a Quantum Ising chain where the transverse magnetization is measured by quantum jumps, our theory predicts a critical phase with logarithmic scaling of the entanglement, an area law phase and a continuous phase transition between them, with an effective central charge vanishing as a square root at the transition point. We compare these predictions with with exact numerical calculations on the same model and find an excellent agreement.