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We relate explicitly the adiabatic curvature -- in flux space -- of aninteracting Hall insulator with nondegenerate ground state to various linearresponse coefficients, in particular the Kubo response and the adiabaticresponse. The flexibility of the setup, allowing for various driving terms andcurrents, reflects the topological nature of the adiabatic curvature. We alsooutline an abstract connection between Kubo response and adiabatic response,corresponding to the fact that electric fields can be generated both byelectrostatic potentials and time-dependent magnetic fields. Our treatment fitsin the framework of rigorous many-body theory, thanks to the gap assumption.

Note on linear response for interacting Hall insulators