We study the effect of spin-orbit interaction on one-dimensional U(1)-invariant frustrated magnets with dominant critical nematic fluctuations. The spin-orbit coupling explicitly breaks the U(1) symmetry of arbitrary global spin rotations about the high-symmetry axis down to $Z_2$ (invariance under a $\pi$ rotation). Given that the nematic order parameter is invariant under a $\pi$ rotation, it is relevant to ask if other discrete symmetries can be spontaneously broken. Here we demonstrate that the spin-orbit coupling induces a bond density wave that spontaneously breaks the translational symmetry and opens a gap in the excitation spectrum.

• Received 11 March 2017
• Revised 16 November 2017

DOI:https://doi.org/10.1103/PhysRevB.96.214408