  We study the interfaces between lattice Laughlin states at different
fillings. We propose a class of model wavefunctions for such systems
constructed using conformal field theory. We find a nontrivial form of charge
conservation at the interface, similar to the one encountered in the field
theory works from the literature. Using Monte Carlo methods, we evaluate the
correlation function and entanglement entropy at the border. Furthermore, we
construct the wavefunction for quasihole excitations and evaluate their mutual
statistics with respect to quasiholes originating at the same or the other side
of the interface. We show that some of these excitations lose their anyonic
statistics when crossing the interface, which can be interpreted as
impermeability of the interface to these anyons. Contrary to most of the
previous works on interfaces between topological orders, our approach is
microscopic, allowing for a direct simulation of e.g. an anyon crossing the
interface. Even though we determine the properties of the wavefunction
numerically, the closed-form expressions allow us to study systems too large to
be simulated by exact diagonalization.
