Unsupervised manifold learning of ground state wave functions

Quantum many-body wave functions are complex objects that encode much information, but it can be challenging to back out the information. In particular, there is no good way to assess whether a given wave function can be a ground state of some local Hamiltonian. Here we employ an unsupervised machine learning algorithm well-suited for discovering trends in high-dimensional space: manifold learning. We apply our approach to a band insulator and the toric code and demonstrate that our approach can separate ground state wave functions from excited state wave functions without any prior knowledge.