Determination of ground-state properties in quantum spin systems by single-qubit unitary operations and entanglement excitation energies

We introduce a method for analyzing ground-state properties of quantum many-body systems, based on the characterization of separability and entanglement by single subsystem unitary operations. We apply the method to the study of the ground-state structure of several interacting spin-1/2 models, described by Hamiltonians with different degrees of symmetry. We show that the approach based on single-qubit unitary operations allows us to introduce ``entanglement excitation energies,'' a set of observables that can characterize ground-state properties, including the quantification of single-site entanglement and the determination of quantum critical points. The formalism allows us to identify the existence and location of factorization points, and a purely quantum ``transition of entanglement'' that occurs at the approach of factorization. This kind of quantum transition is characterized by a diverging ratio of excitation energies associated with single-qubit unitary operations.