On the heart associated with a torsion pair

Given an associative ring R and a torsion pair (T ,F) in the category of right R-modules, the heart H(T,F) associated with (T,F) is an abelian subcategory of the bounded derived category Db(R). In the present paper we deal with the problem of when H(T ,F) is equivalent to a category of modules. We show that if (T,F) is a faithful torsion pair, or, in the general case, if R is right poised and semiperfect, then H(T , F ) is equivalent to a category of modules if and only if T and F are naturally associated with a complex in Db(R) of length two with finitely generated projective terms.