Universal Relations in Long-range Quantum Spin Chains

• URL: http://arxiv.org/abs/2510.23135v1
• Date: Mon, 27 Oct 2025 09:16:10 GMT
• Title: Universal Relations in Long-range Quantum Spin Chains
• Authors: Ning Sun, Lei Feng, Pengfei Zhang,
• Abstract summary: We show that universal relations manifest in a distinct class of quantum many-body systems.<n>Using effective field theory and the operator product expansion, we establish connections between the behavior of equal-time spin correlation functions.<n>Our results could be readily tested in state-of-the-art trapped-ion systems.
• Score: 18.957108140592716
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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