  We give examples of principal algebraic actions of the noncommutative free
group $F$ of rank two, as well as other groups, by automorphisms of a connected
compact abelian group for which there is an explicit measurable isomorphism to
a Bernoulli action of the group. The isomorphism is defined using homoclinic
points, a method that has been used earlier to construct symbolic covers of
algebraic actions. To our knowledge, these are the first nontrivial examples of
the Bernoullicity of an algebraic action of $F$.
