Phase Transitions in the Ferromagnetic Region of the spin-S Bilinear-Biquadratic Spin Chain

We study ferromagnetic region of the spin-S bilinear-biquadratic spin chain. While the spin S=1 case has been massively studied, higher-S case has been less studied. In this study, we focus on the ferromagnetic region in the higher-S case and find an exact phase-transition point between fully polarized ferromagnetic-phase and partially polarized ferromagnetic-phase by using numerical exact-diagonalization method up to S=3. The partially polarized ferromagnetic-phase has fractional magnetization M=1-1/(2S) under zero magnetic-field; for example, M=2/3 for S=3/2, and M=3/4 for S=2. In addition, at a high symmetric point in the partially polarized ferromagnetic-phase, we find rigorous eigen-state correspondence between spin-S model and spin-1/2 antiferromagnetic model, which can be generalized to any dimensional lattices. This is nothing but ``spin-1/2 liquefaction'' of ferromagnet. Even after spontaneous magnetization, the ground state has quantum entanglement due to a spin-1/2 antiferromagnetic quantum state in ferromagnetic classical background. External magnetic field generated by this ``fractional ferromagnet'' has the potential to become a manipulation handle of an entangled quantum state in the context of quantum computer science.