Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries

Abstract

We study quantum many-body systems in the presence of an exotic antiunitary translation or inversion symmetry involving time reversal. Based on a symmetry-twisting method and spectrum robustness, we propose that a half-integer spin chain that respects any of these two antiunitary crystalline symmetries in addition to the discrete ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ global spin-rotation symmetry must either be gapless or possess degenerate ground states. This explains the gaplessness of a class of chiral spin models not indicated by the Lieb-Schultz-Mattis theorem and its known extensions. Moreover, we present symmetry classes with minimal sets of generators that give nontrivial Lieb-Schultz-Mattis-type constraints, argued by the bulk-boundary correspondence in 2D symmetry-protected topological phases as well as lattice homotopy. Our results for detecting the ingappability of 1D quantum magnets from the interplay between spin-rotation symmetries and magnetic space groups are applicable to systems with a broader class of spin interactions, including Dzyaloshinskii-Moriya and triple-product interactions.

arXiv comment5 pages, 2 figures, 1 table; published version up to formatting

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• Parafermionic representation of Potts-based cluster chain