  We introduce a connection between entanglement induced by interaction and
geometric phases acquired by a composite quantum spin system. We begin by
analyzing the evaluation of cyclic (Aharonov-Anandan) and non-cyclic
(Mukunda-Simon) geometric phases for general spin chains evolving in the
presence of time-independent magnetic fields. Then, by considering Heisenberg
chains, we show that the interaction geometric phase, namely, the total
geometric phase with subtraction of free spin contributions, is directly
related to the global (Meyer-Wallach) entanglement exhibited by an initially
separable state during its evolution in Hilbert space. This is analytically
shown for N=2 spins and numerically illustrated for larger chains. This
relationship promotes the interaction geometric phase to an indicator of global
entanglement in the system, which may constitute a useful tool for quantum
tasks based on entanglement as a resource to their performance.
