lower bound for determinant of $(X^TY)$

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Am looking for a lower bound for determinant, $\det(X^TY)$ where $X^T$ is $p \times n$ and $Y$ is $n \times p$. Is it $Tr(X^TY)^{-1}$? Regardless, what are other lower bounds for this? $X,Y$ are real-valued matrices.