  We investigate the tetraquark bound states that are manifestly exotic using
three distinct few-body methods: Gaussian Expansion Method (GEM), Resonating
Group Method (RGM), and Diffusion Monte Carlo (DMC). We refer to manifestly
exotic states that do not involve a mixture with the conventional mesons
through the creation and annihilation of $n\bar{n}$, where $n=u, d$. Our
calculations are conducted with two types of quark models: the pure constituent
quark model featuring one-gluon-exchange interactions and confinement
interactions, and the chiral constituent quark model, supplemented by extra
one-boson-exchange interactions. This study represents a comprehensive
benchmark test of various few-body methods and quark models. Our findings
reveal the superiority of GEM over RGM and DMC methods based on present
implements for the tetraquark bound states. Additionally, we observe a tendency
for the chiral quark model to overestimate the binding energies. We
systematically explore the fully, triply, doubly, and singly heavy tetraquark
states with $J^P=0^+,1^+,2^+$, encompassing over 150 states in total. We
successfully identify several bound states, including
$[cc\bar{n}\bar{n}]_{J^{P}=1^{+}}^{I=0}$,
$[bb\bar{n}\bar{n}]_{J^{P}=1^{+}}^{I=0}$,
$[bc\bar{n}\bar{n}]_{J^{P}=0^{+},1^{+},2^{+}}^{I=0}$,
$[bs\bar{n}\bar{n}]_{J^{P}=0^{+},1^{+}}^{I=0}$,
$[cs\bar{n}\bar{n}]_{J^{P}=0^{+}}^{I=0}$, and
$[bb\bar{n}\bar{s}]_{J^{P}=1^{+}}$, all found to be bound states below the
dimeson thresholds.
