  According to the Onsager's semiclassical quantization rule, the Landau levels
of a band are bounded by its upper and lower band edges at zero magnetic field.
However, there are two notable systems where the Landau level spectra violate
this expectation, including topological bands and flat bands with singular band
crossings, whose wave functions possess some singularities. Here, we introduce
a distinct class of flat band systems where anomalous Landau level spreading
(LLS) appears outside the zero-field energy bounds, although the relevant wave
function is nonsingular. The anomalous LLS of isolated flat bands are governed
by the cross-gap Berry connection that measures the wave-function geometry of
multi bands. We also find that symmetry puts strong constraints on the LLS of
flat bands. Our work demonstrates that an isolated flat band is an ideal system
for studying the fundamental role of wave-function geometry in describing
magnetic responses of solids.
