Abstract: In this talk, we discuss necessary and sufficient conditions for the existence of \(n\)-th chaos of the solution to the parabolic Anderson model \[\frac{\partial}{\partial t}u(t,x)=\frac{1}{2}\Delta u(t,x)+u(t,x)\dot{W}(t,x),\] where \(\dot{W}(t,x)\) is a fractional Brownian field with temporal Hurst parameter \(H_0\ge 1/2\) and spatial parameters \(H\) \( =(H_1, \cdots, H_d)\) \( \in (0, 1)^d\). When \(d=1\), we extend the condition on the parameters under which the chaos expansion of the solution is convergent in the mean square sense, which is both sufficient and necessary under some circumstances.