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

Abstract

Abstract:We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially under point-group operations, their point-group behavior in the band language can be simplified by choosing a suitable Bloch basis. We first give two analytically accessible examples. Then, we show that, for a large class of models, a natural Bloch basis exists, in which the vertex functions in the band language transform trivially under all point-group operations. As a consequence, the point-group symmetries can be used to reduce the computational effort in perturbative many-particle approaches, such as the functional renormalization group.

Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional renormalization group calculation with high-wave-vector resolution

“…This work was financially supported by the DFG research units RTG 1995 and SPP 1459. As a technical side note, it is worth discussing the implications of the choice of Bloch basis [49] in our calculation. By choice of Bloch basis, we are referring to the U(1) invariance of the electronic structure under k-local phase transformations of the fields and vertex functions, which also influences the form taken byT k .…”

“…By choice of Bloch basis, we are referring to the U(1) invariance of the electronic structure under k-local phase transformations of the fields and vertex functions, which also influences the form taken byT k . One would be tempted to work in the so-called proper gauge or proper basis [49], where the local phase is chosen so that all objects inside the integrals in Eq. (18) This is the choice referred to in section IV A when discussing critical onsite interaction strengths.…”

Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

“…where RÔ denotes the representation matrix corresponding to the elementÔ in the point group G. (For a more general discussion of point-group symmetries in multiband models, see Ref. 49.) Here and throughout, we will assume that the parity operation [50] k → −k is contained in G.…”

Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model

“…Ref. 46). The position argument in the real-space form factors then corresponds to the relative distance between the constituents of such a pair, i.e.…”

“…In Ref. 46, two of us have discussed how point-group symmetries manifest themselves in a large class of multiband models. Also the Emery model belongs to that class.…”