Phase diagram of the quantum spin- 12 Heisenberg- Γ model on a frustrated zigzag chain

We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ 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 $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their 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 ${\mathrm{YbCuS}}_{2}$, characterized by gapless excitations and seemingly nonmagnetic behavior.