  Quantum oscillations (QOs) in transport and thermodynamic parameters at high
magnetic fields are an unambiguous signature of the Fermi surface, the defining
characteristic of a metal. Therefore, recent observations of QOs in insulating
SmB$_6$ and YbB$_{12}$, in particular the QOs of the resistivity $\rho_{xx}$ in
YbB$_{12}$, have been a big surprise, pointing to the formation of a novel
state of quantum matter. Despite the large charge gap inferred from the
insulating behaviour of $\rho_{xx}$, these compounds seemingly host a Fermi
surface at high magnetic fields. However, the nature of the ground state in
zero field has been little explored. Here we report the use of low-temperature
heat-transport measurements to discover gapless, itinerant, charge-neutral
excitations in the ground state of YbB$_{12}$. At zero field, despite
$\rho_{xx}$ being far larger than that of conventional metals, a sizable linear
temperature dependent term in the thermal conductivity is clearly resolved in
the zero-temperature limit
($\kappa_{xx}/T(T\rightarrow0)=\kappa_{xx}^0/T\neq0$). Such a residual
$\kappa_{xx}^0/T$ term at zero field, which is absent in SmB$_6$, leads to a
spectacular violation of the Wiedemann-Franz law: the Lorenz ratio
$L=\kappa_{xx}\rho_{xx}/T$ is $10^{4}$-$10^{5}$ times larger than that expected
in conventional metals. These data indicate that YbB$_{12}$ is a charge
insulator but a thermal metal, suggesting the presence of itinerant neutral
fermions. Remarkably, more insulating crystals with larger activation energies
exhibit a larger amplitude of the resistive QOs as well as a larger
$\kappa_{xx}^0/T$, in stark contrast to conventional metals. Moreover, we find
that these fermions couple to magnetic field, despite their charge neutrality.
Our findings expose novel gapless and highly itinerant, charge-neutral
quasiparticles in this unconventional quantum state.
