Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians

The structure of the ground spaces of quantum systems consisting of local
interactions is of fundamental importance to different areas of physics. In
this Letter, we present a necessary and sufficient condition for a subspace to
be the ground space of a k-local Hamiltonian. Our analysis are motivated by the
concept of irreducible correlations studied by [Linden et al., PRL 89, 277906]
and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum
entropy. It establishes a better understanding of the ground spaces of local
Hamiltonians and builds an intimate link of ground spaces to the correlations
of quantum states.