One-dimensional frustrated Heisenberg antiferromagnet of spin 1/2 in a strong magnetic field

The properties of the one-dimensional antiferromagnet of spin 1/2 in a strong magnetic field h with nearest- and next-nearest-neighbor interactions are studied in terms of the equivalent Bose-gas problem. We find that below the first critical field ${\mathit{h}}_{\mathit{c}\mathit{u}}$ the phase with a gap in the elementary excitations spectrum and corresponding plateau in the magnetization curve should exist due to the two-particle attraction in the vicinity of the commensurate wave number ${\mathit{p}}_{0\mathit{u}}$=π. In the interval between the first and second critical fields ${\mathit{h}}_{\mathit{c}\mathit{u}}$h${\mathit{h}}_{\mathit{c}\mathit{f}}$, the system behaves as the one-dimensional Bose gas with particle repulsion and the magnetization has a typical square-root dependence on field.