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Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice

Masaki Oshikawa
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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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Masaki Oshikawa. 1999-11-10. Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice. https://doi.org/10.1103/physrevlett.84.1535

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