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.

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

References in corpus (8)

• Progress and prospects in magnetic topological materials
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• CPT theorem and classification of topological insulators and superconductors
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions

Cited by in corpus (5)

• (SPT-)LSM theorems from projective non-invertible symmetries
• LSM and CPT
• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Parafermionic representation of Potts-based cluster chain