Find the minimum of $x-y$ among all ordered pairs of real numbers $(x, y)$, $x$ and $y$ between 0 and 1, where there exists a real number $a

Find the minimum of $x-y$ among all ordered pairs of real numbers $(x, y)$, $x$ and $y$ between 0 and 1, where there exists a real number $a \neq 1$ such that\[ \log_{x}a + \log_{y}a = 4\log_{xy}a. \]