Model wavefunctions for interfaces between lattice Laughlin states

Błażej Jaworowski, Anne E. B. Nielsen

Published 2019-11-27Version 1

We study the interfaces between lattice Laughlin states at different fillings. Using conformal field theory, we derive analytical wavefunctions for the entire system and restrictions on filling factors under which they are well defined. We find a nontrivial form of charge conservation at the interface. Next, using Monte Carlo methods, we evaluate the entanglement entropy at the border, showing the linear scaling and an additional constant correction to the topological entanglement entropy. 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 these excitations are able to cross the border and stay localized, although their statistics may become ill-defined in such a process. 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 analytical expressions allow us to study systems too large to be simulated by exact diagonalization.