Interactions do not renormalize the phase-space topological expression for the Hall conductivity in a 2+1D tight-binding model with non-uniform magnetic field, to all orders of perturbation theory.
Be- low we will prove that this expression does not receive corrections from interactions, i.e
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Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
Interactions do not renormalize the phase-space topological expression for the Hall conductivity in a 2+1D tight-binding model with non-uniform magnetic field, to all orders of perturbation theory.