  The spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric
and square-plaquette sites is investigated using various analytical and
numerical methods: variational technique, localized-magnon approach, exact
diagonalization (ED) and density-matrix renormalization group (DMRG) method.
The model belongs to the class of flat-band systems and it has a rich
ground-state phase diagram including phases with spontaneously broken
translational symmetry. Moreover, it exhibits an anomalous low-temperature
thermodynamics close to continuous or discontinuous field-driven quantum phase
transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase,
monomer-tetramer phase, localized-magnon phase and two different spin-liquid
phases. If the intra-plaquette coupling is at least twice as strong as the
monomer-plaquette coupling, the variational method furnishes a rigorous proof
of the monomer-tetramer ground state in a low-field region and the
localized-magnon approach provides an exact evidence of a single magnon trapped
at each square plaquette in a high-field region. In the rest of parameter space
we have numerically studied the ground-state phase diagram and magnetization
process using DMRG and ED methods. It is shown that the zero-temperature
magnetization curve may involve up to four intermediate plateaus at zero,
one-fifth, two-fifth and three-fifth of the saturation magnetization, while the
specific heat exhibits a striking low-temperature peak in a vicinity of
discontinuous quantum phase transitions.
