  Recent discovery of the half quantized thermal Hall conductivity in
$\alpha$-RuCl$_3$, a candidate material for the Kitaev spin liquid, suggests
the presence of a highly entangled quantum state in external magnetic fields.
This field induced phase appears between the low field zig-zag magnetic order
and the high field polarized state. Motivated by this experiment, we study
possible field induced quantum phases in theoretical models of the Kitaev
magnets, using the two dimensional tensor network approach or infinite tensor
product states. We find various quantum ground states in addition to the chiral
Kitaev spin liquid occupying a small area in the phase diagram. They form a
band of emergent quantum phases in an intermediate window of external magnetic
fields, somewhat reminiscent of the experiment. We discuss the implications of
these results in view of the experiment and previous theoretical studies.
