  The mixed spin-1 and spin-1/2 Heisenberg octahedral chain with regularly
alternating monomeric spin-1 sites and square-plaquette spin-1/2 sites is
investigated using variational technique, localized-magnon approach, exact
diagonalization (ED) and density-matrix renormalization group (DMRG) method.
The investigated model has in a magnetic field an extraordinarily rich
ground-state phase diagram, which includes the uniform and cluster-based
Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, two quantum spin
liquids and two bound magnon crystals in addition to the fully polarized
ferromagnetic phase. The lowest-energy eigenstates in a highly-frustrated
parameter region belong to flat bands and hence, low-temperature thermodynamics
above the bound magnon-crystal ground states can be satisfactorily described
within the localized-magnon approach. The variational method provides an exact
evidence for the magnon-crystal phase with a character of the monomer-tetramer
ground state at zero field, while another magnon-crystal phase with a single
bound magnon at each square plaquette is found in a high-field region. A
diversity of quantum ground states gives rise to manifold zero-temperature
magnetization curves, which may involve up to four wide intermediate plateaus
at zero, one-sixth, one-third and two-thirds of the saturation magnetization,
two quantum spin-liquid regions and two tiny plateaus at one-ninth and
one-twelfth of the saturation magnetization corresponding to the fragmentized
cluster-based Haldane phases.
