Analytic correspondence between multipartite entanglement and quantum phase transitions

We derive an analytic correspondence between multipartite concentratable entanglement (CE) and quantum phase transitions in one-dimensional quantum spin systems. We prove that CE shares the same analyticity structure as generalized order parameters, identifies the same quantum phases, and, for Gaussian ground states, is completely determined by the same single-particle correlation matrix. Numerical validation on the transverse-field Ising and generalized cluster-Ising models confirms these analytical predictions for both symmetry-breaking and symmetry-protected topological quantum phase transitions. Since CE can be measured directly using a constant-depth parallelized SWAP-test circuit, our results establish CE as an experimentally accessible, model-independent probe of quantum phase transitions without requiring model-specific order parameters.