Long-range interacting systems are locally non-interacting

TL;DR

This paper proves that in the thermodynamic limit, long-range interacting quantum systems behave as locally non-interacting, with dynamics that do not generate correlations, impacting their relaxation and thermalization properties.

Contribution

It establishes that in the strong long-range regime, local properties are described by an emergent non-interacting theory, a novel insight into long-range quantum systems.

Findings

Local properties are described by a non-interacting theory in the thermodynamic limit.

System dynamics factorize, preventing correlation generation over time.

Implications for relaxation, quasi-stationary states, and thermalization in long-range systems.

Abstract

Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fuelling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions, long-range interacting systems display novel physics, such as nonlinear light cones for the propagation of information or inequivalent thermodynamic ensembles. In this work, we consider generic long-range open quantum systems in arbitrary dimensions and focus on the so-called strong long-range regime. We prove that in the thermodynamic limit local properties, captured by reduced quantum states, are described by an emergent non-interacting theory. Here, the dynamics factorizes and the individual constituents of the system evolve independently such that no correlations are generated over time. In this sense, long-range interacting systems are locally non-interacting. This has significant implications for their relaxation behavior, for instance in relation to the emergence of long-lived quasi-stationary states or to the absence of thermalization.