Nonsymmorphic spin-space cubic groups and SU(2)$_1$ conformal invariance in one-dimensional spin-1/2 models

Abstract

Recently, extended gapless phases with emergent SU(2)_11 conformal invariance occupying finite regions in the phase diagrams have been found in one-dimensional spin-1/2 models with nonsymmorphic O_hOh symmetry groups. In this work, we investigate the question of whether the conditions for emergent SU(2)_11 invariance can be loosened. We find that besides the nonsymmorphic O_hOh group, the other four smaller nonsymmorphic cubic groups including OO, T_hTh, T_dTd and TT can also give rise to emergent SU(2)_11 invariance. Minimal spin-1/2 models having these nonsymmorphic cubic groups as symmetry groups are constructed, and numerical evidences for the emergent SU(2)_11 invariance are provided. Our work is useful for understanding gapless phases in one-dimensional spin systems with nonsymmorphic symmetries.