Universal Relations in Long-range Quantum Spin Chains

TL;DR

This paper demonstrates that universal relations, akin to those in ultracold gases, also appear in long-range quantum spin chains, linking correlations, structure factors, and contact density.

Contribution

It establishes the presence of universal relations in long-range quantum spin chains using effective field theory and numerical simulations.

Findings

Universal relations connect spin correlations and contact density.

Theoretical predictions are verified via matrix product state simulations.

Results are applicable to trapped-ion experimental systems.

Abstract

Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems, embodying the ``from few to many'' philosophy. An intriguing example is the set of universal relations in ultracold atomic gases, which connect a wide range of observables to a single quantity known as the contact. In this Letter, we demonstrate that universal relations manifest in a distinct class of quantum many-body systems, long-range quantum spin chains, which belong to a completely new universality class. Using effective field theory and the operator product expansion, we establish connections between the asymptotic behavior of equal-time spin correlation functions, the dynamical structure factor, and the contact density. The theoretical predictions for equal-time correlators are explicitly verified through numerical simulations based on matrix product states. Our results could be readily tested in state-of-the-art trapped-ion systems.