Nearly-linear light cones in long-range interacting quantum systems

TL;DR

This paper proves that in long-range quantum systems with power-law interactions, the influence of local perturbations grows algebraically rather than exponentially, establishing nearly-linear light cones for certain interaction strengths.

Contribution

It demonstrates that light cones in long-range interacting quantum systems are algebraic for lpha > 2D, contradicting previous exponential growth assumptions.

Findings

Light cones are algebraic for lpha > 2D.

Light cones become linear as lpha   lpha   lpha ightarrow    lpha ightarrow    lpha ightarrow   .

Constraints on correlation growth and entanglement in long-range systems.

Abstract

In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems.