  The Kitaev model, which hosts a quantum spin liquid (QSL) in the ground
state, was originally defined on a two-dimensional honeycomb lattice, but can
be straightforwardly extended to any tricoordinate lattices in any spatial
dimensions. In particular, the three-dimensional (3D) extensions are of
interest as a realization of 3D QSLs, and some materials like
$\beta$-Li$_{2}$IrO$_{3}$, $\gamma$-Li$_2$IrO$_3$, and $\beta$-ZnIrO$_{3}$ were
proposed for the candidates. However, the phase diagrams of the models for
those candidates have not been fully elucidated, mainly due to the limitation
of numerical methods for 3D frustrated quantum spin systems. Here we study the
Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, by using the
pseudofermion functional renormalization group method. We show that the
ground-state phase diagram contains the QSL phases in the vicinities of the
pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four
magnetically ordered phases, similar to the two-dimensional honeycomb case. Our
results respect the four-sublattice symmetry inherent in the model, which was
violated in the previous study. Moreover, we also show how the phase diagram
changes with the anisotropy in the interactions. The results provide a
reference for the search of the hyperhoneycomb Kitaev materials.
