Quantum correlations and entanglement in far-from-equilibrium spin systems

TL;DR

This paper explores how correlations and entanglement develop over time in far-from-equilibrium spin-1/2 XXZ models with variable-range interactions, using analytic and numerical methods applicable across dimensions.

Contribution

It provides a comprehensive analysis of the dynamical emergence of quantum correlations and entanglement in these models, highlighting universal behaviors and experimental realizations.

Findings

Identification of a non-perturbative dynamic singularity in 1D correlation functions

Universal power-law exponent characterizing the singularity

Discussion of experimental platforms for realizing these models

Abstract

By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments, and can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: we characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a non-perturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed.