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Symmetry 2013, 5(4), 313-343; doi:10.3390/sym5040313

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

1,2,* , 1,2
1 Institute for Theoretical Solid State Physics, RWTH Aachen University, Aachen D-52056, Germany 2 JARA-FIT, Fundamentals of Future Information Technology, Jülich 52425, Germany 3 National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
* Author to whom correspondence should be addressed.
Received: 8 October 2013 / Revised: 30 October 2013 / Accepted: 4 November 2013 / Published: 11 November 2013
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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.
Keywords: correlated electrons; point-group symmetries; functional renormalization group correlated electrons; point-group symmetries; functional renormalization group
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Maier, S.A.; Honerkamp, C.; Wang, Q.-H. Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models. Symmetry 2013, 5, 313-343.

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