%0 Journal Article %D 2010 %T Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Mary Beth Ruskai %A Bei Zeng %A Duanlu Zhou %X 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. %8 2010/10/13 %G eng %U http://arxiv.org/abs/1010.2739v4