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We perform the energy spectra calculating for the $S$-wave $\bar{Q}Q\bar{q}q$(where $Q=c,b$ and $q=u,d,s$) system within two constituent quark models. Thebound states of $B^*\bar{B}^*$ with $I(J^{PC})=1(0^{++}),~1(1^{+-}),~0(2^{++})$and $B\bar{B}^*$ with isospin $I=1$, or $0$ are obtained incolor-singlet-singlet channel. If considering the coupling of color channels,apart from the deep bound states appear in $[b\bar{q}]^{(*)}[q\bar{b}]^{(*)}$scenario, a bound state $[c\bar{q}]^*[q\bar{c}]^*$ with $I(J^{PC})=1(0^{++})$is also formed. The $B\bar{B}^*$ and the $B^*\bar{B}^*$ with quantum number$1(1^{+-})$ are well candidates for $Z_b^{\pm}(10610)$ and $Z_b^{\pm}(10650)$reported by Belle collaboration respectively, while the $B\bar{B}^*$ withisospin $0$ can be interpret as a candidate for $Z_b^{0}(10610)$. A bound state$[c\bar{q}]^*[q\bar{c}]^*$ with $I(J^{PC})=1(0^{++})$ is comparable with$Z_c^{+}(4025)$ announced by BES.

Dynamical study of $S$-wave $\bar{Q}Q\bar{q}q$ system