Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
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abstract
Combined with Laughlin's argument on the quantized Hall conductivity, Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number, on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength and particle statistics (bose/fermi), a finite excitation gap is possible only when the particle number per unit cell of the groundstate is an integer.
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The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.