  Motivated by recent experiments on $\alpha$-RuCl$_3$, we investigate a
possible quantum spin liquid ground state of the honeycomb-lattice spin model
with bond-dependent interactions. We consider the $K-\Gamma$ model, where $K$
and $\Gamma$ represent the Kitaev and symmetric-anisotropic interactions
between spin-1/2 moments on the honeycomb lattice. Using the infinite density
matrix renormalization group (iDMRG), we provide compelling evidence for the
existence of quantum spin liquid phases in an extended region of the phase
diagram. In particular, we use transfer matrix spectra to show the evolution of
two-particle excitations with well-defined two-dimensional dispersion, which is
a strong signature of quantum spin liquid. These results are compared with
predictions from Majorana mean-field theory and used to infer the quasiparticle
excitation spectra. Further, we compute the dynamical structure factor using
finite size cluster computations and show that the results resemble the
scattering continuum seen in neutron scattering experiments on
$\alpha$-RuCl$_3$. We discuss these results in light of recent and future
experiments.
