  We study a system of qubits that are coupled to each other via only one
degree of freedom represented, e.g., by $\sigma_z$-operators. We prove that, if
by changing the Hamiltonian parameters, a non-degenerate ground state of the
system is continuously transformed in such a way that the expectation values of
$\sigma_z$ operators of at least two coupled qubits change, this ground state
is entangled. Using this proof, we discuss connection between energy level
anticrossings and ground state entanglement. Following the same line of
thought, we introduce entanglement witnesses, based on cross-susceptibilities,
that can detect ground state entanglement for any bipartition of the
multi-qubit system. A witness for global ground state entanglement is also
introduced.
