Spread of correlations in long-range interacting quantum systems

TL;DR

This paper investigates how correlations spread in long-range quantum systems, revealing three distinct dynamical regimes depending on the decay exponent, and challenges traditional notions of locality in quantum information propagation.

Contribution

It provides a comprehensive analysis of correlation dynamics in long-range Ising models, identifying regimes with light cone-like, weakly long-range, and instantaneous correlation spreading.

Findings

For >2, correlations exhibit a light cone similar to short-range systems.

For 1<<2, correlations spread without a clear light cone but with finite propagation speed.

For <1, correlations propagate instantaneously, breaking Lieb-Robinson bounds.

Abstract

The non-equilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power-law with distance $\propto r^{-\alpha}$, $\alpha>0$. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for $\alpha>2$; weakly long-range for $1<\alpha<2$ without a clear light cone but with a finite propagation speed of almost all excitations; and fully non-local for $\alpha<1$ with instantaneous transmission of correlations. This last regime breaks generalized Lieb--Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasi-particles remains valid, allowing an intuitive interpretation of our findings via divergences of quasi-particle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.