Generating Generalized Ground-State <i>Ansätze</i> from Few-Body Examples

We introduce a method that generates ground-state Ansätze for quantum many-body systems that are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor network states via an evolutionary algorithm. This language provides operations that allow the generated tensor network states to automatically scale with system size. Consequently, we can evaluate Ansatz fitness for small systems, which is computationally efficient, while favoring structures that continue to perform well with increasing system size. This ensures that the Ansatz captures robust features of the ground-state structure. Remarkably, we find analytically tractable Ansätze with a degree of universality, which encode correlations, capture finite-size effects, accurately predict ground-state energies, and offer a good description of critical phenomena. We demonstrate this method on the Lipkin-Meshkov-Glick model and the quantum transverse-field Ising model, where the same Ansatz was independently generated for both. The simple structure of the Ansatz allows us to obtain exact expressions for the expectation values of local observables as well as for correlation functions. In addition, it permits symmetries that are broken in the Ansatz to be restored, which provides a systematic means of improving the accuracy of the Ansatz.