We show that multipartite entanglement can be used as an efficient way to identify the critical points of $1+1\mathrm{D}$ systems. We demonstrate this with the quantum Ising model, lattice $\lambda {\varphi }^4$ approximated with qutrits, and arrays of Rydberg atoms. To do so, we use multipartite compositions of entanglement quantities—$S_A$,$S_B$,$S_C$,$S_{AB}$,$S_{BC}$, and $S_{ABC}$—combined to form the strong subadditivity, weak monotonicity, and a convex combination of these with conformal properties. We will demonstrate how these bipartite entanglement quantities of a quadpartite system display behavior at phase boundaries, but the combination of these aforementioned quantities sharpens and localizes this behavior at the boundaries even better. We will show that we can extend a scheme for approximating the entanglement with the mutual information, and that this acts as a lower bound for the individual bipartite quantities. We show the mutual information will also follow the changes in the entanglement for the above combined quantities, despite no longer being a strict lower bound and the additional contributions of different signs. This mutual information approximation to the identifying quantities can have its lower probabilities removed in a process we call filtering, and despite the combination of terms with different signs, will respond well to the filtering and offer improvements to the lower bound.

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• Conformal field theory
• Entanglement entropy
• Lattice field theory
• Quantum entanglement
• Quantum information theory