The low-lying light tetraquark states with quantum numbers $J^P=0^{+}$, $1^{+}$ and $2^{+}$

The low-lying light tetraquark states are investigated in the non-relativistic quark model (NRQM) including the pseudoscalar meson exchange, where two different confinement potential schemes, the Cornell potential and the linear potential, are employed, along with the instanton-induced interaction serving as the residual spin-dependent interaction. The numerical results show agreement with masses of $f_0(500)$, $f_0(1370)$, $f_0(1500)$, $f_0(2020)$, $f_0(2200)$, $h_1(1170)$, $h_1(1595)$, $h_1(1900)$, $h_1(1965)$, $h_1(2215)$, $f_2(1430)$, $f_2(1640)$, $f_2(1810)$, $f_2(2010)$, $f_2(2150)$, $a_0(980)$, $a_0(1450)$, $a_0(1950)$, $a_1(1260)$, $a_1(1640)$, $a_2(1700)$, $K_0^{\ast }(1430)$, $K_0^{\ast }(1950)$, $K_1(1270)$, $K_1(1440)$, $K_1(1650)$, and $K_2^{\ast }(1980)$. The results shed light on the spectrum of these mesons and offer guidande to search for the tetraquarks in the future.