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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Quantum Magnetism

Background:

  • Quantum many-body systems often exhibit complex behaviors governed by symmetries.
  • The Lieb-Schultz-Mattis theorem provides fundamental constraints on gapped phases in spin chains.
  • Exotic antiunitary symmetries, including time reversal, introduce novel physical phenomena.

Purpose of the Study:

  • To investigate the implications of antiunitary translation or inversion symmetries in quantum many-body systems.
  • To determine the ground state properties of half-integer spin chains with combined spin-rotation and antiunitary crystalline symmetries.
  • To extend the understanding of gaplessness conditions beyond the standard Lieb-Schultz-Mattis theorem.

Main Methods:

  • Symmetry-twisting method applied to analyze ground state properties.
  • Spectrum robustness analysis to infer gaplessness or degeneracy.
  • Investigation of bulk-boundary correspondence in 2D symmetry-protected topological phases.
  • Lattice homotopy arguments for symmetry classification.

Main Results:

  • A half-integer spin chain with antiunitary crystalline symmetries (translation/inversion) and Z_{2}×Z_{2} spin-rotation symmetry is shown to be either gapless or possess degenerate ground states.
  • This finding explains the gaplessness of chiral spin models not covered by existing theorems.
  • Minimal symmetry classes providing nontrivial Lieb-Schultz-Mattis-type constraints are identified.
  • Conditions for detecting the 'ingappability' of 1D quantum magnets are established.

Conclusions:

  • The interplay of spin-rotation symmetries and magnetic space groups dictates fundamental properties of 1D quantum magnets.
  • The results are applicable to a broad range of spin interactions, including Dzyaloshinskii-Moriya and triple-product interactions.
  • This work provides a theoretical framework for understanding exotic phases in quantum magnetism.