Ferromagnetic Haldane state in an S=2 bilinear-biquadratic spin system on an orthogonal-dimer chain

We present a theory of the realization of a ferromagnetic Haldane state in an S=2 bilinear-biquadratic (BLBQ) model on an orthogonal-dimer chain. The coexistence of a ferromagnetic state and a Haldane state is due to the "eigensystem embedding," i.e., the rigorous correspondence between a subset of the eigenstates in the S=2 BLBQ model and the entire set of the eigenstates in the S=1/2 Heisenberg model [1]. Exact-diagonalization calculations indicate that the ground state in the BLBQ model is a fractionally magnetized M = 3/4 Haldane state and the excitations of the ferromagnetic Haldane state consist from Haldane gap excitation and magnon like gapless mode [2]. Moreover, a ferromagnetic-dimer multiplet state is an exact ground state on the BLBQ model on an orthogonal dimer chain. The eigensystem embedding demonstrates that a quantum ferromagnet can be obtained for an arbitrary spin S >= 2 in any dimension and for any lattice.