  The $S=1/2$ Kitaev honeycomb model has attracted significant attention as an
exactly solvable example with a quantum spin liquid ground state. In a properly
oriented external magnetic field, chiral Majorana edge modes associated with a
quantized thermal Hall conductance emerge, and a distinct spin-disordered phase
appears at intermediate field strengths, below the polarized phase. However,
since material realizations of Kitaev magnetism invariably display competing
exchange interactions, the stability of these exotic phases with respect to
additional couplings is a key issue. Here, we report a 24-site exact
diagonalization study of the Heisenberg-Kitaev model in a magnetic field
applied in the [001] and [111] directions. By mapping the full phase diagram of
the model and contrasting the results to recent nonlinear spin-wave
calculations, we show that both methods agree well, thus establishing that
quantum corrections substantially modify the classical phase diagram.
Furthermore, we find that, in a [111] field, the intermediate-field
spin-disordered phase is remarkably stable to Heisenberg interactions and may
potentially end in a novel quantum tricritical point.
