Entanglement dynamics of monitored noninteracting fermions on graphics processing units

TL;DR

This study uses GPU techniques to analyze entanglement dynamics in monitored noninteracting fermions, revealing the presence of measurement-induced phase transitions in 1D and 2D systems.

Contribution

It demonstrates the effectiveness of GPU-based simulations for large lattice sizes, providing new insights into entanglement behavior and phase transitions beyond existing theoretical predictions.

Findings

In 1D, large lattice sizes are needed to confirm the absence of MIPT.

In 2D, a MIPT occurs at finite monitoring rate with a scale-invariant mutual information.

Critical exponent for the MIPT is approximately 1.3, consistent across protocols.

Abstract

The description of the entanglement dynamics of monitored noninteracting fermions, including the existence of measurement-induced phase transitions (MIPTs), is a challenging problem with conflicting results in the literature. The mapping of the problem onto a non-linear sigma model (NLSM) indicates that relatively large lattice sizes are required to determine the nature of the entanglement entropy (EE) in the thermodynamics limit. Here we address this problem numerically for monitored noninteracting fermions with $U(1)$ symmetry. The use of graphics processing unit (GPU) techniques, even with outdated hardware, makes it possible to reach much larger lattice sizes ($L = 16384$ and $160\times160$ in one (1d) and two (2d) dimensions respectively) than in previous studies which enables us to characterize quantitatively the entanglement dynamics. In 1d, we show that in order to confirm the absence of a MIPT, for both projective and homodyne measurements, predicted by the NLSM it is necessary to reach $L \sim 10000$. In 2d, also as predicted by the NLSM, we observe for both protocols a MIPT at finite monitoring rate characterized by a scale invariant mutual information. The critical monitoring strength depends on the protocol while the critical exponent $\nu \approx 1.3$ governing the approach to the MIPT is similar in both cases. These features are not correctly predicted by the NLSM. Our results paves the way for a fully quantitative description of the entanglement dynamics of monitoring quantum systems.