  We use the diffusion Monte Carlo method to calculate the doubly heavy
tetraquark $T_{cc}$ system in two kinds of constituent quark models, the pure
constituent quark model AL1/AP1 and the chiral constituent quark model. When
the discrete configurations are complete and no spatial clustering is preseted,
the AL1/AP1 model gives an energy of $T_{cc}$ close to the $DD^*$ threshold,
and the chiral constituent quark model yields a deeply bound state. We further
calculate all doubly heavy tetraquark systems with $J^P=0^+,1^+,2^+$, and
provide the binding energies of systems with bound states. The $I(J^P)=0(0^+)$
$bc\bar{n}\bar{n}$, $0(1^+)$ $bb\bar{n}\bar{n}$, $0(1^+)$ $bc\bar{n}\bar{n}$,
$\frac{1}{2}(1^+)$ $bb\bar{s}\bar{n}$ systems have bound states in all three
models. Since the DMC method has almost no restriction on the spatial part, the
resulting bound states have greater binding energies than those obtained in
previous works.
