Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian

TL;DR

This paper investigates how different unravelings of the same Lindblad equation affect entanglement scaling in a quantum Ising chain with dephasing, revealing contrasting behaviors and phase diagrams.

Contribution

It compares two Gaussian-preserving unravelings of the Lindblad equation, showing they produce different entanglement scaling and phase diagrams in the quantum Ising chain.

Findings

One unraveling shows a crossover from area-law to logarithm-law entanglement.

The other unraveling exhibits only logarithm-law entanglement.

Non-Hermitian evolution predictions conflict with unraveling results.

Abstract

We study the dynamics of entanglement in the quantum Ising chain with dephasing dissipation in a Lindblad master equation form. We consider two unravelings which preserve the Gaussian form of the state, allowing to address large system sizes. The first unraveling gives rise to a quantum-state-diffusion dynamics, while the second one describes a specific form of quantum-jump evolution, suitably constructed to preserve Gaussianity. In the first case we find a crossover from area-law to logarithm-law entanglement scaling and draw the related phase diagram. In the second case we only find logarithm-law scaling, remarking the different entanglement behavior for different unravelings of the same Lindblad equation. Finally, we compare these outcomes with the predictions of a non-Hermitian Hamiltonian evolution, finding conflicting results.