  The spin-1/2 Ising-Heisenberg branched chain composed of regularly
alternating Ising spins and Heisenberg dimers involving an additional side
branching is rigorously solved in a magnetic field by the transfer-matrix
approach. The ground-state phase diagram, the magnetization process and the
concurrence measuring a degree of bipartite entanglement within the Heisenberg
dimers are examined in detail. Three different ground states were found
depending on a mutual interplay between the magnetic field and two different
coupling constants: the modulated quantum antiferromagnetic phase, the quantum
ferrimagnetic phase and the classical ferromagnetic phase. Two former quantum
ground states are manifested in zero-temperature magnetization curves as
intermediate plateaus at zero and one-half of the saturation magnetization,
whereas the one-half plateau disappears at a triple point induced by a strong
enough ferromagnetic Ising coupling. The ground-state phase diagram and
zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg
branched chain were investigated using DMRG calculations. The latter fully
quantum Heisenberg model involves, besides two gapful phases manifested as zero
and one-half magnetization plateaus, gapless quantum spin-liquid phase. The
intermediate one-half plateau of the spin-1/2 Heisenberg branched chain
vanishes at Kosterlitz-Thouless quantum critical point between gapful and
gapless quantum ground states unlike the triple point of the spin-1/2
Ising-Heisenberg branched chain.
