Abstract
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.
Highlights
One of the most striking characteristics of topological orders is the bulk-boundary correspondence—the fact that the bulk properties of the given phase can be inferred from its physics at the edge
In this work we focus on Laughlin-Laughlin interfaces, for which the matrix product state (MPS) construction was not yet demonstrated
In this work we have presented a class of model wave functions for interfaces between lattice Laughlin states
Summary
One of the most striking characteristics of topological orders is the bulk-boundary correspondence—the fact that the bulk properties of the given phase can be inferred from its physics at the edge. It provides concrete examples of states belonging to the general classes determined by the top-down methods, which allows us to test the predictions from these works and to investigate the nonuniversal properties of these states Such an approach can either rely on diagonalizing Hamiltonians, or on proposing model wave functions. Such constructions are widely used in the case of single quantum Hall states (i.e., without interface) since the seminal work of Laughlin [75] For such systems, they have proven useful, as they can be studied both analytically and numerically, and for the latter, the considered system sizes can be much larger than in exact diagonalization. Instead of expressing vertex operators of the two CFTs as MPS matrices as in [26,27,83], we patch them together directly In this way we construct the model wave functions for ground state and localized bulk quasihole excitations.
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