  Fully-heavy tetraquark states, i.e. $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$,
$bb\bar{c}\bar{c}$ ($cc\bar{b}\bar{b}$), $cb\bar{c}\bar{c}$,
$cb\bar{b}\bar{b}$, and $cb\bar{c}\bar{b}$, are systematically investigated by
means of a non-relativistic quark model based on lattice-QCD studies of the
two-body $Q\bar{Q}$ interaction, which exhibits a spin-independent Cornell
potential along with a spin-spin term. The four-body problem is solved using
the Gaussian expansion method; additionally, the so-called complex scaling
technique is employed so that bound, resonance, and scattering states can be
treated on the same footing. Moreover, a complete set of four-body
configurations, including meson-meson, diquark-antidiquark, and K-type
configurations, as well as their couplings, are considered for spin-parity
quantum numbers $J^{P(C)}=0^{+(+)}$, $1^{+(\pm)}$, and $2^{+(+)}$ in the
$S$-wave channel. Several narrow resonances, with two-meson strong decay widths
less than 30 MeV, are found in all of the tetraquark systems studied.
Particularly, the fully-charm resonances recently reported by the LHCb
Collaboration, at the energy range between 6.2 and 7.2 GeV in the di-$J/\psi$
invariant spectrum, can be well identified in our calculation. Focusing on the
fully-bottom tetraquark spectrum, resonances with masses between 18.9 and 19.6
GeV are found. For the remaining charm-bottom cases, the masses are obtained
within a energy region from 9.8 GeV to 16.4 GeV. All these predicted resonances
can be further examined in future experiments.
