  The characterization of quantum spin liquid phases in Kitaev materials has
been a subject of intensive studies over the recent years, both theoretically
and experimentally. Most theoretical studies have focused on an isotropically
interacting model with its coupling strength being equivalent on each bond in
an attempt to simplify the problem. Here, we study an extended spin-1/2
Kitaev-$\Gamma$ model on a honeycomb lattice with an additional tuning
parameter that controls the coupling strength on one of the bonds: we connect
the limit of isolated Kitaev-$\Gamma$ chains, which is known to exhibit an
emergent $SU(2)_1$ Tomonaga-Luttinger liquid phase [Yang et al. Phys. Rev.
Lett. {\bf 124}, 147205 (2020)], to the two-dimensional model. We report on an
instance, in which the Tomonaga-Luttinger liquid persists for finite
inter-chain coupling. A quantum spin liquid phase develops in analogy to
\emph{sliding Luttinger liquids} that differs from the Kitaev spin liquid. This
quantum spin liquid phase features spinon-like excitations similar to those of
the antiferromatnetic Heisenberg chain. We use numerical Exact Diagonalization
and Density Matrix Renormalization Group on various cluster geometries in a
complementary way to overcome finite-size limitations.
