  Taking the quantum electrodynamics (QED) effect into account, we study the
black hole phase transition and Ruppeiner geometry for the Euler-Heisenberg
anti-de Sitter black hole in the extended phase space. For negative and small
positive QED parameter, we observe a small/large black hole phase transition
and reentrant phase transition, respectively. While a large positive value of
the QED parameter ruins the phase transition. The phase diagrams for each case
are explicitly exhibited. Then we construct the Ruppeiner geometry in the
thermodynamic parameter space. Different features of the corresponding scalar
curvature are shown for both the small/large black hole phase transition and
reentrant phase transition cases. Of particular interest is that an additional
region of positive scalar curvature indicating dominated repulsive interaction
among black hole microstructure is present for the black hole with a small
positive QED parameter. Furthermore, the universal critical phenomena are also
observed for the scalar curvature of the Ruppeiner geometry. These results
indicate that the QED parameter has a crucial influence on the black hole phase
transition and microstructure.
