In this work, we perform a detailed study on the consequences of
nonsymmorphic symmetries in the Luttinger phase of the one-dimensional spin-1/2
Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction.
Nonsymmorphic bosonization formulas for the spin operators are proposed,
containing ten non-universal coefficients which are determined by our density
matrix renormalization group simulations to a high degree of accuracy. Using
the nonsymmorphic bosonization formulas, different Fourier components and decay
powers in the correlation functions are disentangled, the response to weak
magnetic fields is analyzed, and the zigzag magnetic order in two dimensions is
recovered from a system of weakly coupled chains. We also find a line of
critical points with an emergent SU(2)1​ conformal symmetry located on the
boundary of the Luttinger liquid phase, where a nonabelian version of
nonsymmorphic bosonization should be applied.Comment: 22 pages, 7 figure