Semiorthogonal decompositions of projective spaces from small quantum cohomology

In a recent article Halpern-Leistner defines the notion of quasi--convergent path in the space of Bridgeland stability conditions. Such a path induces a semiorthogonal decomposition of the derived category. We investigate quasi-convergent paths in the stability manifold of projective spaces and answer positively to two questions posed by Halpern-Leistner. We construct quasi-convergent paths that start from the geometric region of the stability space and whose central charge is given by a fundamental solution of the quantum differential equation. We also construct quasi-convergent paths whose central charges are the quantum cohomology central charges defined by Iritani.