  The orbital magnetic susceptibility of an electron gas in a periodic
potential depends not only on the zero field energy spectrum but also on the
geometric structure of cell-periodic Bloch states which encodes interband
effects. In addition to the Berry curvature, we explicitly relate the orbital
susceptibility of two-band models to a quantum metric tensor defining a
distance in Hilbert space. Within a simple tight-binding model allowing for a
tunable Bloch geometry, we show that interband effects are essential even in
the absence of Berry curvature. We also show that for a flat band model, the
quantum metric gives rise to a very strong orbital paramagnetism.
