  We give a short review of our recent works on the first-order quantum phase
transitions in frustrated spin chains with orthogonal-dimer structure. When the
ratio of the competing antiferromagnetic exchange couplings is varied, a
first-order transition occurs between the dimer phase and the plaquette phase,
which is accompanied by the discontinuity in the spin excitation gap. We
further show that strong frustration triggers the phase transitions in a
magnetic field, which exhibit plateaus and jumps in the magnetization curve.
The hole-doping effect is also addressed for the orthogonal-dimer chain with
linked-tetrahedra structure. It is found that the competing antiferromagnetic
interactions result in a first-order metal-insulator transition upon hole
doping.
