# Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions

## TL;DR

This paper investigates universal scaling laws governing how correlations spread in quantum systems with both short- and long-range interactions, revealing a double-structured, velocity-dependent behavior after a quench.

## Contribution

It introduces a unified framework for correlation spreading in quantum systems, deriving universal exponents and velocities applicable to various interaction ranges and excitation spectra.

## Key findings

- Correlation edge spreads with velocity twice the maximum group velocity.
- For long-range interactions, correlation edge spreads slower than ballistic.
- Maxima of correlations propagate faster or ballistically depending on system gap.

## Abstract

We study the spreading of information in a wide class of quantum systems, with variable-range interactions. We show that, after a quench, it generally features a double structure, whose scaling laws are related to a set of universal microscopic exponents that we determine. When the system supports excitations with a finite maximum velocity, the spreading shows a twofold ballistic behavior. While the correlation edge spreads with a velocity equal to twice the maximum group velocity, the dominant correlation maxima propagate with a different velocity that we derive. When the maximum group velocity diverges, as realizable with long-range interactions, the correlation edge features a slower-than-ballistic motion. The motion of the maxima is, instead, either faster-than-ballistic, for gapless systems, or ballistic, for gapped systems. The phenomenology that we unveil here provides a unified framework, which encompasses existing experimental observations with ultracold atoms and ions. It also paves the way to simple extensions of those experiments to observe the structures we describe in their full generality.