Ground-state factorization in spin-1/2 systems by single qubit unitary operations and entanglement excitation energies

We analyze the ground state properties of models of interacting Spin-1/2 systems by introducing a novel formalism of suitably defined single-qubit unitary operations (SQUOs). Such a framework allows to identify a new class of energy observable, the energy associated to the excitations above the ground state that are produced when the latter is modified by the action of a SQUO We show that tracking the behavior of this kind of energy observable allows to single out and characterize quantum critical points in an ample class of quantum spin-1/2 models. We then show how the squared distance of a quantum state from the set of all its possible images under the action of SQUOs coincides with the linear entropy (tangle) of the state. and that the excitation energy corresponding to the distance is a monotonic function of the von Neumann entropy of entanglement (single-site entanglement. or block entanglement between a single spin and the rest of the system) Hence, the excitation energy associated to the extremal SQUO holds the property of vanishing if and only if the quantum ground state is completely separable This particular excitation energy is then identified as the "entanglement excitation energy" (EXE). We discuss the implications of our results for the observable characterization of ground state entanglement and separability, in particular the exact determination of fully factorized ground states in non-exactly solvable models, and the possibility of introducing new analytic techniques for the study of ground state physics via controlled expansions in powers of the EXEs around quantum factorization points