Magnetization plateau in the $S=$$\frac{1}{2}$ Heinsenberg spin chain with next-nearest-neighbor and alternating nearest-neighbor interactions

The magnetization process of the $S=1/2\mathrm{}$ Heisenberg chain with next-nearest-neighbor (NNN) and alternating nearest-neighbor interactions is investigated using the bosonization technique. The existence of the NNN interaction is shown to stabilize a “diluted” dimer order at magnetization $m^z=1/4,$ leading to a plateau, where two degenerate ground states appear. Effective Hamiltonians describing the low-energy physics in the vicinity of the $m^z=1/4\mathrm{}$ plateau are also presented. The analogy to metal-insulator transitions is discussed briefly.