  In this work, we systematically calculate the mass spectra of the $S$-wave
fully heavy tetraquark states $bb\bar b\bar b$, $cc\bar c\bar c$, and $bb\bar
c\bar c$ in two nonrelativistic quark models. A tetraquark state may be an
admixture of a $6_c-\bar 6_c$ state and a $\bar 3_c-3_c$ one, where $6_c-\bar
6_c$($\bar 3_c-3_c$) denotes the color configuration with a $6_c$ ($\bar 3_c$)
diquark and a $\bar 6_c$ ($3_c$) antidiquark. For the tetraquark states $bb\bar
b\bar b$ and $cc\bar c\bar c$ with $J^{PC}={0^{++}}$, the $6_c-\bar 6_c$ state
is lower than the $\bar 3_c-3_c$ one in both the two quark models, while the
order of the $bb\bar c\bar c$ states depend on models. The $6_c-\bar 6_c$ and
$\bar 3_c-3_c$ mixing effects are induced by the hyperfine interactions between
the diquark and antidiquark, while the contributions from the
one-gluon-exchange (OGE) Coulomb or the linear confinement potentials vanish
for the $QQ\bar Q'\bar Q'$ system. With the couple-channel effects, we obtain
the similar mass spectra. The numerical results show that the ground $QQ\bar
Q'\bar Q'$ ($Q=b,c$ and $Q'=b,c$) tetraquark states are located above the
corresponding scattering states, which indicates that there may not exist a
bound state in the scheme of the two quark models.
