Reconstructing the spatial structure of quantum correlations in materials

Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of a general family of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at an arbitrary mutual distance. Using neutron scattering data for the compound <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>KCuF</a:mi><a:mn>3</a:mn></a:msub></a:math>—a system of weakly coupled <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>S</b:mi><b:mo>=</b:mo><b:mn>1</b:mn><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:math> Heisenberg chains—and numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a different emergent length scale—the quantum coherence length—which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials. Published by the American Physical Society 2024