Spin nematic phase in (quasi-)one-dimensional frustrated magnet in strong magnetic field

We discuss spin-1/2 one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor $J_1$ and antiferromagnetic next-nearest-neighbor $J$ exchange interactions in strong magnetic field $H$. It is well known that due to attraction between magnons quantum phase transitions (QPTs) take place at $H=H_s$ from the fully polarized phase to nematic ones if $J>|J_1|/4$. Such a transition at $J>0.368|J_1|$ is characterized by softening of the two-magnon bound-state spectrum. Using a bond operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations which spectrum coincides at $H\ge H_s$ with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at $H=H_s$ makes substantially standard the QPT consideration. In 1D case at $H<H_s$, we find an expression for the magnetization which describes well existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before either in the limiting case of $J\gg|J_1|$ or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the $H$--$T$ plane between the fully polarized and the nematic phases is given by $H_s(0)-H_s(T)\propto T^{3/2}$. Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to $1/\ln(1+|J_1|/J)$. Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel.