Phase Diagram and Quantum Entanglement Properties of a Pentamer S = 1/2 Heisenberg Spin Cluster.

Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S=1/2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement.