Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks

TL;DR

This paper explores measurement-induced entanglement transitions in the Quantum Ising chain, revealing a universal transition from a critical to an area-law phase under different measurement protocols, with implications for understanding non-Hermitian quantum dynamics.

Contribution

It compares two measurement protocols in the Quantum Ising chain, showing similar entanglement transitions and analyzing the critical behavior and universality classes.

Findings

Identified a sharp entanglement transition at the same measurement rate in both protocols.

Observed a continuous vanishing of the effective central charge at the transition.

Revealed bimodal entanglement statistics near the critical point.

Abstract

We investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment. We compare two different limits of the measurement problem, the stochastic quantum-state diffusion protocol corresponding to infinite small jumps per unit of time and the no-click limit, corresponding to post-selection and described by a non-Hermitian Hamiltonian. In both cases we find a remarkably similar phenomenology as the measurement strength $\gamma$ is increased, namely a sharp transition from a critical phase with logarithmic scaling of the entanglement to an area-law phase, which occurs at the same value of the measurement rate in the two protocols. An effective central charge, extracted from the logarithmic scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting different universality classes for the two protocols. We interpret the central charge mismatch near the transition in terms of noise-induced disentanglement, as suggested by the entanglement statistics which displays emergent bimodality upon approaching the critical point. The non-Hermitian Hamiltonian and its associated subradiance spectral transition provide a natural framework to understand both the extended critical phase, emerging here for a model which lacks any continuous symmetry, and the entanglement transition into the area law.