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We analyze the point-group symmetries of generic multiband tight-bindingmodels with respect to the transformation properties of the effectiveinteractions. While the vertex functions in the orbital language may transformnon-trivially under point-group operations, their point-group behavior in theband language can be simplified by choosing a suitable Bloch basis.We firstgive two analytically accessible examples. Then we show that, for a large classof models, a natural Bloch basis exists, in which the vertex functions in theband language transform trivially under all point-group operations. As aconsequence, the point-group symmetries can be used to reduce the computationaleffort in perturbative many-particle approaches such as the functionalrenormalization group.

Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models