Title: Magnetization jump in one dimensional $J-Q_{2}$ model with anisotropic exchange,
Abstract: We investigate the adiabatic magnetization process of the one-dimensional
$J-Q_{2}$ model with XXZ anisotropy $g$ in an external magnetic field $h$ by
using density matrix renormalization group (DMRG) method. According to the
characteristic of the magnetization curves, we draw a magnetization phase
diagram consisting of four phases. For a fixed nonzero pair coupling $Q$, i)
when $g<-1$, the ground state is always ferromagnetic in spite of $h$; ii) when
$g>-1$ but still small, the whole magnetization curve is continuous and smooth;
iii) if further increasing $g$, there is a macroscopic magnetization jump from
partially- to fully-polarized state; iv) for a sufficiently large $g$, the
magnetization jump is from non- to fully-polarized state. By examining the
energy per magnon and the correlation function, we find that the origin of the
magnetization jump is the condensation of magnons and the formation of magnetic
domains. We also demonstrate that while the experienced states are
Heisenberg-like without long-range order, all the \textit{jumped-over} states
have antiferromagnetic or Néel long-range orders, or their mixing.