Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians

Details Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians

2010-10-13

arxiv.org/abs/1010.2739v3

Physics

Quantum Physics

This paper has been withdrawn by the author due to a crucial error in proof of "only if" part. We will write a note to explain

Scientific paper

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.

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