  In the field of quantum magnetism, the exactly solvable Kitaev honeycomb
model serves as a paradigm for the fractionalization of spin degrees of freedom
and the formation of $\mathbb{Z}_2$ quantum spin liquids. An intense
experimental search has led to the discovery of a number of spin-orbit
entangled Mott insulators that realize its characteristic bond-directional
interactions and, in the presence of magnetic fields, exhibit no indications of
long-range order. Here, we map out the complete phase diagram of the Kitaev
model in tilted magnetic fields and report the emergence of a distinct gapless
quantum spin liquid at intermediate field strengths. Analyzing a number of
static, dynamical, and finite temperature quantities using numerical exact
diagonalization techniques, we find strong evidence that this phase exhibits
gapless fermions coupled to a massless $U(1)$ gauge field. We discuss its
stability in the presence of perturbations that naturally arise in spin-orbit
entangled candidate materials.
