We study the ground-state properties of a spin-1/2 model on a chain containing four-spin Ising-like interactions in the presence of both transverse and longitudinal magnetic fields. We use entanglement entropy and finite-size scaling methods to obtain the phase diagrams of the model. Our numerical calculations reveal a rich variety of phases and the existence of multicritical points in the system. We identify phases with both ferromagnetic and antiferromagnetic orderings. We also find periodically modulated orderings formed by a cluster of like spins followed by another cluster of opposite like spins. The quantum phases in the model are found to be separated by either first- or second-order transition lines.
By combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising-like quantum antiferromagnet
BaCo2V2O8 in a longitudinal magnetic field applied along the Ising anisotropy, which is also the chain direction. The external field closes the excitation gap due to the magnetic anisotropy, inducing a transition from the N\'eel ordered state to an incommensurate longitudinal spin density wave phase. If the field is increased further, another transition into a transverse antiferromagnetic phase takes place at 9 T due to the competition between longitudinal and transverse correlations. We numerically and experimentally show that the model of XXZ chains connected by a weak interchain interaction well reproduces this transition. We also calculate the dynamical susceptibility and demonstrate that it agrees quantitatively with inelastic neutron scattering measurements. In contrast to the abrupt change of magnetic ordering, the spectra do not change much at the transition at 9 T, and the spin dynamics can be described as a Tomonaga-Luttinger liquid. We also refine the modeling of
BaCo2V2O8 by including a four-site periodic term arising from the crystal structure which enables one to account for an anomaly of the magnetic susceptibility appearing at 19.5 T, as well as for the anticrossing observed in the inelastic neutron scattering spectra.