One-to-one correspondence between two-point correlators and entanglement in magnetic systems

Résumé :

There are multiple measures of multipartite entanglement — including entanglement in thermal mixtures — currently used to study many-body interacting systems. Recently, Quantum Fisher Information has been proposed as a multipartite entanglement measure that can be connected to experimentally accessible observables. In this talk, I will present our recent findings about a one-to-one correspondence between two-point correlators and a certain general class of Heisenberg-like Hamiltonians and wavefunctions. This is a foundation of our claim that a mapping from finite-temperature observables to any entanglement measure exists for such systems. Furthermore, I will present our results of training a convolutional neural network (CNN) to recognize and predict the entanglement for one-dimensional anisotropic XY and XYZ models, which exhibit an entanglement transition. From our preliminary results we found that entanglement can be accurately predicted by a CNN using both static and dynamical correlators, even when the network is trained on only a fraction of the full dataset or on data from a different system than the one used for prediction. Specifically, when trained on observables from an anisotropic XY model, accurate predictions can be achieved using only about 3% (6%) of the data when employing dynamical two-point correlators (structure factors) for learning.

Contact : pierre.nataf@lpmmc.cnrs.fr