  Despite their fundamental importance in dictating the quantum mechanical
properties of a system, ground states of many-body local quantum Hamiltonians
form a set of measure zero in the many-body Hilbert space. Hence determining
whether a given many-body quantum state is ground-stateable is a challenging
task. Here we propose an unsupervised machine learning approach, dubbed the
Entanglement Clustering ("EntanCl"), to separate out ground-stateable wave
functions from those that must be excited state wave functions using
entanglement structure information. EntanCl uses snapshots of an ensemble of
swap operators as input and projects this high dimensional data to
two-dimensions, preserving important topological features of the data
associated with distinct entanglement structure using the uniform manifold
approximation and projection (UMAP). The projected data is then clustered using
K-means clustering with $k=2$. By applying EntanCl to two examples, a
one-dimensional band insulator and the two-dimensional toric code, we
demonstrate that EntanCl can successfully separate ground states from excited
states with high computational efficiency. Being independent of a Hamiltonian
and associated energy estimates, EntanCl offers a new paradigm for addressing
quantum many-body wave functions in a computationally efficient manner.
