Interfaces between topologically distinct phases of matter reveal a
remarkably rich phenomenology. To go beyond effective field theories, we study
the prototypical example of such an interface between two Abelian states,
namely the Laughlin and Halperin states. Using matrix product states, we
propose a family of model wavefunctions for the whole system including both
bulks and the interface. We show through extensive numerical studies that it
unveils both the universal properties of the system, such as the central charge
of the gapless interface mode and its microscopic features. It also captures
the low energy physics of experimentally relevant Hamiltonians. Our approach
can be generalized to other phases described by tensor networks.Comment: Published version. Former supplementary material has been extended
and published as a separate articl