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Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models
Institute for Theoretical Solid State Physics, RWTH Aachen University, Aachen D-52056, Germany
JARA-FIT, Fundamentals of Future Information Technology, Jülich 52425, Germany
National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
* Author to whom correspondence should be addressed.
Received: 8 October 2013; in revised form: 30 October 2013 / Accepted: 4 November 2013 / Published: 11 November 2013
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.
Keywords: correlated electrons; point-group symmetries; functional renormalization group
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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.
Maier SA, Honerkamp C, Wang Q-H. Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models. Symmetry. 2013; 5(4):313-343.
Maier, Stefan A.; Honerkamp, Carsten; Wang, Qiang-Hua. 2013. "Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models." Symmetry 5, no. 4: 313-343.