Magnetic susceptibility of interacting free and Bloch electrons

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Abstract
The form of the magnetic-susceptibility formula given by Roth and by Wannier and Upadhyaya for noninteracting Bloch electrons is generalized to include all many-body effects. The arguments used do not involve any approximations and are entirely based on the translational-symmetry property of the system. Spin and orbital susceptibility of some well-known cases, Fermi liquid and strongly correlated electrons in a narrow band, are shown to follow from the most general formula for the magnetic susceptibility of interacting free and Bloch (with or without spin-orbit coupling) electrons derived in this paper.

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