By integrating out fermions in gapped Dirac Hamiltonian, one can obtain a topological term for topological insulator. Why there is no further correction to this term when electron-electron interaction is included?
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$\begingroup$ The coefficient of these terms must be quantized(usually by gauge invariance). So imagine there is some correction from electron-electron interaction, as long as the gap is maintained, the coefficient must change continuously, so it just stays the same unless a phase transition takes place. $\endgroup$– Meng ChengCommented Apr 14, 2015 at 14:15
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$\begingroup$ @Meng Cheng Thanks! I know this argument. But is there any proof or explanation from Feynmann diagram point of view? $\endgroup$– qc2014Commented Apr 14, 2015 at 14:26
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$\begingroup$ For the case of Hall conductivity, you can prove that diagrammatically using Ward identity. Let me see whether I can find a reference.... $\endgroup$– Meng ChengCommented Apr 14, 2015 at 14:28
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$\begingroup$ @Meng Cheng Thanks for providing me the clue, Meng. I think I have found one myself. link. They do apply Ward Identity which is valid under electron-electron interaction. But I am still little confused in their way of calculating current-current correlation function. It seems like they 'dress' both vertices. As far as I know, the Kubo formula in the interaction case only dress one vertex. But maybe that is an unrelated problem. $\endgroup$– qc2014Commented Apr 14, 2015 at 15:57
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