Phase diagram of the quantum spin-1/2 Heisenberg- model on a frustrated zigzag chain

We investigate the quantum spin-1/2 zigzag chain with frustrated J₁-J₂ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the -term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite -term, we observe the persistent dimer singlet state of the J₁-J₂ Heisenberg model, sustaining a nonzero spin gap, while also giving rise to a new gapless branch of nonmagnetic excitation. This gapless mode induces robust nematic fluctuations manifesting in its long-ranged correlations, however, the true condensation does not occur until the -term becomes comparable with the Heisenberg term. There, the nonmagnetic phases transform into Ising-type ferromagnetic or antiferromagnetic long-range orders that arise from the -term spontaneously selecting magnetic easy axes. Its orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS₂, characterized by gapless excitations and seemingly nonmagnetic behavior accompanied by incommensurate correlations.