Spreading of Correlations and Entanglement in the Long-Range Transverse Ising Chain

TL;DR

This paper investigates how correlations and entanglement spread in a long-range transverse Ising chain, revealing a weak form of causality with diverse propagation behaviors depending on the observable.

Contribution

It demonstrates the emergence of a non-universal causality in long-range quantum systems using advanced tensor-network methods and analytic calculations.

Findings

Local spin correlations are sub-ballistic

Entanglement entropy propagates ballistically

Causal edges depend on the observable and interaction range

Abstract

Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by non-universal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or super-ballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.