Space group symmetries and low lying excitations of many-body systems at integer fillings

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However the set of all points at which the localized tightbinding orbitals are located will not in the cases we are interested in, form a Bravais lattice, rather they corresponds to a Bravais lattice with a basis

Cited in the paper.

It is sufficient to consider one element from each translation coset g ​ 𝒯 g\mathcal{T} where 𝒯 \mathcal{T} is the invariant subgroup of lattice translations of G G

Cited in the paper.

These points need not coincide with the points 𝐤 s \mathbf{k}_{s} associated with the single group

Cited in the paper.

This may happen for instance, if the system is invariant under arbitrary S ​ U ​ ( 2 ) SU(2) rotations in addition to the space group transformations

Cited in the paper.

We have learned that parallel work by Parameswaran et al. related to these topics has recently been posted on the arXiv at arXiv:1212.0557v2

Original

Cited in the paper.

M. B. Hastings, Phys. Rev. B 69

2004

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We will also need to impose certain restrictions on the size, a feature that is shared by proofs of the higher dimensional extensions of the Lieb Schultz Mattis theorem Oshikawa 2000 ; Hastings 2004

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M. B. Hastings, EPL (Europhysics Letters) 70

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