Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians

TL;DR

This paper establishes a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian, linking ground spaces to quantum correlations through the maximum entropy principle.

Contribution

It provides a novel criterion for identifying ground spaces of local Hamiltonians based on maximum entropy and correlation concepts.

Findings

Provides a complete characterization of ground spaces for local Hamiltonians.

Connects ground space structure to quantum correlations and maximum entropy principles.

Enhances understanding of quantum many-body ground state properties.

Abstract

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.