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 quantum correlation
functions, which express the degree of quantum coherence in the fluctuations of
two spins at arbitrary mutual distance. Using neutron scattering data on the
compound KCuF3​\unicode{x2014} a system of weakly coupled S=1/2
Heisenberg chains \unicode{x2014} and of 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 new emergent length of quantum-mechanical origin \unicode{x2014}
the quantum coherence length \unicode{x2014} 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.Comment: Main text: 8 pages, 5 figures. Supplementary information: 4 pages, 5
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