Shaping Causality: Emergence of Nonlocal Light Cones in Long-Range Quantum Systems

TL;DR

This paper analytically explores how long-range quantum interactions can be engineered to control the emergence of local and nonlocal light cones, enabling programmable information spread in quantum systems.

Contribution

It derives an effective Hamiltonian identifying the interaction terms responsible for nonlocality, allowing precise control over the causal landscape in long-range quantum systems.

Findings

Large interaction strength or system size enables nonlocal signals at distant points.

Initial conditions can be tuned to generate programmable nonlocal correlations.

The work provides a framework for designing causal structures in quantum information devices.

Abstract

While for non-relativistic short-range interactions, the spread of information is local, remaining confined in an effective light cone, long-range interactions can generate either nonlocal (faster-than-ballistic) or local (ballistic) spread of correlations depending on the initial conditions. This makes long-range interactions a rich platform for controlling the spread of information. Here, we derive an effective Hamiltonian analytically and identify the specific interaction term that drives nonlocality in a wide class of long-range spin chains. This allows us to understand the conditions for the emergence of local behavior in the presence of nonlocal interactions and to identify a regime where the causal space-time landscape can be precisely designed. Indeed, we show that for large long-range interaction strength or large system size, initial conditions can be chosen in a way that allows a local perturbation to generate nonlocal signals at programmable distant positions, which then propagate within effective light cones. The possibility of engineering the emergence of nonlocal Lieb-Robinson-like light cones allows one to shape the causal landscape of long-range interacting systems, with direct applications to quantum information processing devices, quantum memories, error correction, and information transport in programmable quantum simulators.